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Operator Gauge Transformations in Nonrelativistic Quantum Electrodynamics

Description: A system of nonrelativistic charged particles and radiation is canonically quantized in the Coulomb gauge and Maxwell's equations in quantum electrodynamics are derived. By requiring form invariance of the Schrodinger equation under a space and time dependent unitary transformation, operator gauge transformations on the quantized electromagnetic potentials and state vectors are introduced. These gauge transformed potentials have the same form as gauge transformations in non-Abelian gauge field theories. A gauge-invariant method for solving the time-dependent Schrodinger equation in quantum electrodynamics is given. Maxwell's equations are written in a form which holds in all gauges and which has formal similarity to the equations of motion of non-Abelian gauge fields. A gauge-invariant derivation of conservation of energy in quantum electrodynamics is given. An operator gauge transformation is made to the multipolar gauge in which the potentials are expressed in terms of the electromagnetic fields. The multipolar Hamiltonian is shown to be the minimally coupled Hamiltonian with the electromagnetic potentials in the multipolar gauge. The model of a charged harmonic oscillator in a single-mode electromagnetic field is considered as an example. The gauge-invariant procedure for solving the time-dependent Schrodinger equation is used to obtain the gauge-invariant probabilities that the oscillator is in an energy eigenstate For comparison, the conventional approach is also used to solve the harmonic oscillator problem and is shown to give gauge-dependent amplitudes.
Date: December 1982
Creator: Gray, Raymond Dale
Partner: UNT Libraries

Test of Gauge Invariance: Charged Harmonic Oscillator in an Electromagnetic Field

Description: The gauge-invariant formulation of quantum mechanics is compared to the conventional approach for the case of a one-dimensional charged harmonic oscillator in an electromagnetic field in the electric dipole approximation. The probability of finding the oscillator in the ground state or excited states as a function of time is calculated, and the two approaches give different results. On the basis of gauge invariance, the gauge-invariant formulation of quantum mechanics gives the correct probability, while the conventional approach is incorrect for this problem. Therefore, expansion coefficients or a wave function cannot always be interpreted as probability amplitudes. For a physical interpretation as probability amplitudes the expansion coefficients must be gauge invariant.
Date: August 1980
Creator: Wen, Chang-tai
Partner: UNT Libraries

Low energy gauge couplings in grand unified theories and high precision physics

Description: I generalize the leading log relations between low energy SU(3){sub QCD}, SU(2){sub {rvec I}} and U(l){sub Y} effective gauge couplings to include all one-loop threshold effects of matter fields in oblique vector self energy quantum corrections for both supersymmetric and non-supersymmetric SU(5) grand unified theories. These always involve an exactly conserved current from the unbroken SU(3){sub QCD} {times} U(L){sub QED} subgroup; this fact strongly constrains any non-decoupling of heavy states as well as the generic character of threshold effects. Relations between low energy gauge couplings depend on the details of the spectra of both the superheavy and low mass sectors; I display the common origin of the logs appropriate to superheavy matter states, which can be found with well known renormalization group techniques, and the combination of logs and polynomials appropriate for light matter states, which cannot. Relations between any two or all three low energy effective gauge couplings do not depend on the top quark or standard model Higgs` masses. Neither do they depend on neutral color singlet states such as other neutral color singlet Higgs` or higgsinos, neutrinos, zinos or photinos. Further, they do not depend on degenerate SU(5) matter representations, of either spin 0 or spin 1/2 of any mass; matter representations of SU(5) can affect such relations only if there is mass splitting within them. The b quark splitting from the {tau} and {nu}{sub {tau}} can affect the relation between gauge couplings for {vert_bar}q{sub 2}{vert_bar} {yields} m{sub b}{sup 2} as can hadronic resonances and multi-hadron states for lower {vert_bar}q{sub 2}{vert_bar}. New mass-split representations of light states, such as occur in supersymmetric theories, can also affect such relations.
Date: September 1, 1993
Creator: Lynn, B. W.
Partner: UNT Libraries Government Documents Department

Effective theory approach to unstable particles

Description: The authors present a novel treatment of resonant massive particles appearing as intermediate states in high energy collisions. The approach uses effective field theory methods to treat consistently the instability of the intermediate resonant state. As a result gauge invariance is respected in every step and calculations can in principle be extended to all orders in perturbation theory, the only practical limitation in going to higher orders being the standard difficulties related to multi-loop integrals. The authors believe that the longstanding problem related to the treatment of instability of particles is now solved.
Date: May 19, 2003
Creator: Zanderighi, Giulia
Partner: UNT Libraries Government Documents Department

A Gauge-Invariant Energy Variational Principle Application to Anisotropic Excitons in High Magnetic Fields

Description: A new method is developed for treating atoms and molecules in a magnetic field in a gauge-invariant way using the Rayleigh-Ritz energy variational principle. The energy operator depends on the vector potential which must be chosen in some gauge. In order to adapt the trial wave function to the gauge of the vector potential, the trial wave function can be multiplied by a phase factor which depends on the spatial coordinates. When the energy expectation value is minimized with respect to the phase function, the equation for charge conservation for stationary states is obtained. This equation can be solved for the phase function, and the solution used in the energy expectation value to obtain a gauge-invariant energy. The method is applicable to all quantum mechanical systems for which the variational principle can be applied. It ensures satisfaction of the charge conservation condition, a gauge-invariant energy, and the best upper bound to the ground-state energy which can be obtained for the form of trial wave function chosen.
Date: December 1983
Creator: Kennedy, Paul K. (Paul Kevin)
Partner: UNT Libraries

Gauge invariance in 2Pi effective actions

Description: (Abstract damaged) The 2PI (two particle irreducible) effective action is a general field theoretic tool for addressing this problem. In constructing it one introduces sources for both the fields and their two-point bilinears.
Date: January 1, 2003
Creator: Mottola, E. (Emil)
Partner: UNT Libraries Government Documents Department

The confining N = 1 supersymmetric gauge theories: A review

Description: The authors give a classification and overview of the confining N = 1 supersymmetric gauge theories. For simplicity they consider only theories based on simple gauge groups and no tree-level superpotential. Classification of these theories can be done according to whether or not there is a superpotential generated for the confined degrees of freedom. The theories with the superpotential include s-confining theories and also theories where the gauge fields participate in the confining spectrum, while theories with no superpotential include theories with a quantum deformed moduli space and theories with an affine moduli space.
Date: August 1, 1998
Creator: Csaki, C.
Partner: UNT Libraries Government Documents Department

M theory fivebrane and SQCD

Description: A low energy effective theory of parallel D(irichlet) branes is a gauge theory with sixteen supercharges, but one can consider a web of brane to realize situations with reduced number of supersymmetry. In this talk, the authors discusses four-dimensional theories with N = 1 and 2 supersymmetry (i.e. four and eight supercharges). In the case of theories with N = 2 supersymmetry, the exact description of the Coulomb branch is given by reinterpreting the web of branes as a configuration of a single fivebrane in the IIA theory. Recently the authors studied the case with N = 1 supersymmetry, and found that description in terms of the fivebrane in M Theory captures strong coupling dynamics of the N = 1 gauge theory in four dimensions. In particular, they found that the configuration of the fivebrane geometrically encodes information on the Affleck-Dine-Seiberg superpotential and the structure of the quantum moduli space of vacua.
Date: September 1, 1997
Creator: Ooguri, H.
Partner: UNT Libraries Government Documents Department

Local discrete symmetries from superstring derived models

Description: Discrete and global symmetries play an essential role in many extensions of the Standard Model, for example, to preserve the proton lifetime, to prevent flavor changing neutral currents, etc. An important question is how can such symmetries survive in a theory of quantum gravity, like superstring theory. In a specific string model the author illustrates how local discrete symmetries may arise in string models and play an important role in preventing fast proton decay and flavor changing neutral currents. The local discrete symmetry arises due to the breaking of the non-Abelian gauge symmetries by Wilson lines in the superstring models and forbids, for example dimension five operators which mediate rapid proton decay, to all orders of nonrenormalizable terms. In the context of models of unification of the gauge and gravitational interactions, it is precisely this type of local discrete symmetries that must be found in order to insure that a given model is not in conflict with experimental observations.
Date: October 1, 1996
Creator: Faraggi, A.E.
Partner: UNT Libraries Government Documents Department

A lattice formulation of chiral gauge theories

Description: We present a method for implementing gauge theories of chiral fermions on the lattice. Discussed topics include: the lattice as a UV regulator, a chiral QED model, modification of the fermion determinant, large gauge-field momenta, and a non-perturbative problem.
Date: August 1, 1996
Creator: Bodwin, G.T.
Partner: UNT Libraries Government Documents Department

Kinematical twist-3 effects in DVCS as a quark spin rotation

Description: We point out that the kinematical twist-3 contributions to the DVCS amplitude, required to restore electromagnetic gauge invariance of the twist-2 amplitude up to O(t/q{sup 2}), can be understood as a spin rotation applied to the twist-2 quark density matrix in the target. This allows for a compact representation of the twist-3 effects, as well as for a simple physical interpretation.
Date: June 1, 2001
Creator: Radyushkin, A.V. & Weiss, C.
Partner: UNT Libraries Government Documents Department

Gauges for the Ginzburg-Landau equations of superconductivity

Description: This note is concerned with gauge choices for the time-dependent Ginzburg-Landau equations of superconductivity. The requiations model the state of a superconducting sample in a magnetic field near the critical tempeature. Any two solutions related through a ``gauge transformation`` describe the same state and are physically indistinquishable. This ``gauge invariance`` can be exploited for analtyical and numerical purposes. A new gauge is proposed, which reduces the equations to a particularly attractive form.
Date: December 31, 1995
Creator: Fleckinger-Pelle, J. & Kaper, H.G.
Partner: UNT Libraries Government Documents Department

QCD with chiral 4-fermion interactions ({chi}QCD)

Description: Lattice QCD with staggered quarks is augmented by the addition of a chiral 4-fermion interaction. The Dirac operator is now non-singular at m{sub q}=0, decreasing the computing requirements for light quark simulations by at least an order of magnitude. We present preliminary results from simulations at finite and zero temperatures for m{sub q}=0, with and without gauge fields. Chiral QCD enables simulations at physical u and d quark masses with at least an order of magnitude saving in CPU time. It also enables simulations with zero quark masses which is important for determining the equation of state. A renormalization group analysis will be needed to continue to the continuum limit. 7 refs., 2 figs.
Date: October 1, 1996
Creator: Kogut, J.B. & Sinclair, D.K.
Partner: UNT Libraries Government Documents Department

Gaugino condensation, loop corrections and S-duality constraint

Description: This talk is a brief review of gaugino condensation in superstring effective field theories and some related issues (such as renormalization of the gauge coupling in the effective supergravity theories and modular anomaly cancellation). As a specific example, we discuss a model containing perturbative (1-loop) corrections to the K{umlt a}hler potential and approximate S-duality symmetry.
Date: November 1, 1996
Creator: Saririan, K.
Partner: UNT Libraries Government Documents Department

A guide to flat direction analysis in anomalous U(1) models

Description: The authors suggest a systematic procedure to study D- and F-flat directions in a large class of models with an anomalous U(1). This class of models is characterized by the existence of a vacuum that breaks all Abelian gauge symmetries connecting the observable sector to the hidden sector. They show that, under some conditions, there is no other stable vacuum that breaks these symmetries. As a consequence, the model yields definite (order of magnitude) predictions for low-energy mass hierarchies. Then they study generic flat directions and identify the ones that may lead to undesirable vacua. They give necessary conditions for those to be lifted, and show that supersymmetry breaking only slightly affects the conclusions from the flat direction analysis.
Date: December 1, 1997
Creator: Irges, N. & Lavignac, S.
Partner: UNT Libraries Government Documents Department

A lattice formulation of chiral gauge theories

Description: The authors present a method for formulating gauge theories of chiral fermions in lattice field theory. The method makes use of a Wilson mass to remove doublers. Gauge invariance is then restored by modifying the theory in two ways: the magnitude of the fermion determinant is replaced with the square root of the determinant for a fermion with vector-like couplings to the gauge field; a double limit is taken in which the lattice spacing associated with the fermion field is taken to zero before the lattice spacing associated with the gauge field. The method applies only to theories whose fermions are in an anomaly-free representation of the gauge group. They also present a related technique for computing matrix elements of operators involving fermion fields. Although the analyses of these methods are couched in weak-coupling perturbation theory, it is argued that computational prescriptions are gauge invariant in the presence of a nonperturbative gauge-field configuration.
Date: December 1, 1995
Creator: Bodwin, G.T.
Partner: UNT Libraries Government Documents Department

M-theory model-building and proton stability

Description: The authors study the problem of baryon stability in M theory, starting from realistic four-dimensional string models constructed using the free-fermion formulation of the weakly-coupled heterotic string. Suitable variants of these models manifest an enhanced custodial gauge symmetry that forbids to all orders the appearance of dangerous dimension-five baryon-decay operators. The authors exhibit the underlying geometric (bosonic) interpretation of these models, which have a Z{sub 2} x Z{sub 2} orbifold structure similar, but not identical, to the class of Calabi-Yau threefold compactifications of M and F theory investigated by Voisin and Borcea. A related generalization of their work may provide a solution to the problem of proton stability in M theory.
Date: September 1, 1997
Creator: Ellis, J.; Faraggi, A.E. & Nanopoulos, D.V.
Partner: UNT Libraries Government Documents Department

Reduce phase space quantization of Ashtekar's gravity on de Sitter background

Description: The authors solve perturbative constraints and eliminate gauge freedom for Ashtekar's gravity on de Sitter background. They show that the reduced phase space consists of transverse, traceless, symmetric, fluctuations of the triad and of transverse, traceless, symmetric fluctuations of the connection. A part of gauge freedom corresponding to the conformal Killing vectors of the three-manifold can be fixed only by imposing conditions on Lagrange multiplier. The reduced phase space is equivalent to that of ADM gravity on the same background.
Date: May 1, 1994
Creator: Grigentch, I. & Vassilevich, D.V.
Partner: UNT Libraries Government Documents Department

O(1/M{sup 3}) effects for heavy-light mesons in lattice NRQCD

Description: The masses of spin-singlet and spin-triplet S-wave mesons containing a single heavy quark are computed in the quenched approximation. The light quark action and gauge field action are both classically-improved and tadpole-improved, and the couplings to the heavy quark are organized by the 1/M expansion of tadpole-improved NRQCD. At each of two lattice spacings, near 0.22fm and 0.26fm, meson masses are obtained for heavy quarks spanning the region between charmed and bottom mesons. Results up to O(1/M), O(1/M{sup 2})and O(1/M{sup 3}) are displayed separately, so that the convergence of the heavy quark expansion can be discussed. Also, the effect of each term in the O(1/M{sup 3}) contribution is computed individually. For bottom mesons the 1/M-expansion appears to be satisfactory, but the situation for charmed mesons is less clear.
Date: March 1998
Creator: Lewis, Randy & Woloshyn, R. M.
Partner: UNT Libraries Government Documents Department

Massless fermions on the lattice

Description: The authors consider a nonlocal lattice action for fermions fermion doubling in lattice theories. It is shown, that it is possible to avoid the fermionic doubling in the case of free fermions, but this approach does not reproduce results for the effective action for gauge fields in the continuum theory, because the high frequency fermion modes have a strong dependence on the gauge field.
Date: December 1, 1994
Creator: Belyaev, V.M.
Partner: UNT Libraries Government Documents Department

Factorization and effective action for high-energy scattering in QCD

Description: The author demonstrates that the amplitude of the high-energy scattering can be factorized in a convolution of the contributions due to fast and slow fields. The fast and slow fields interact by means of Wilson-line operators -- infinite gauge factors ordered along the straight line. The resulting factorization formula gives a starting point for a new approach to the effective action for high-energy scattering.
Date: April 1, 1998
Creator: Balitsky, Ian
Partner: UNT Libraries Government Documents Department

Wilson loops in minimal surfaces

Description: The AdS/CFT correspondence suggests that the Wilson loop of the large N gauge theory with N = 4 supersymmetry in 4 dimensions is described by a minimal surface in AdS{sub 5} x S{sup 5}. The authors examine various aspects of this proposal, comparing gauge theory expectations with computations of minimal surfaces. There is a distinguished class of loops, which the authors call BPS loops, whose expectation values are free from ultra-violet divergence. They formulate the loop equation for such loops. To the extent that they have checked, the minimal surface in AdS{sub 5} x S{sup 5} gives a solution of the equation. The authors also discuss the zig-zag symmetry of the loop operator. In the N = 4 gauge theory, they expect the zig-zag symmetry to hold when the loop does not couple the scalar fields in the supermultiplet. They will show how this is realized for the minimal surface.
Date: April 27, 1999
Creator: Drukker, Nadav; Gross, David J. & Ooguri, Hirosi
Partner: UNT Libraries Government Documents Department

Searches for new gauge bosons at future colliders

Description: The search reaches for new gauge bosons at future hadron and lepton colliders are summarized for a variety of extended gauge models. Experiments at these energies will vastly improve over present limits and will easily discover a Z` and/or W` in the multi-TeV range.
Date: September 1, 1996
Creator: Rizzo, T.G.
Partner: UNT Libraries Government Documents Department

On the anomalous U(1) in free fermionic superstring models

Description: The realistic free fermionic models have had an intriguing success in explaining different properties of the observed particle spectrum. In this paper the authors discuss in some detail the anomalous U(1) symmetry which exists in these models. They study the properties of the anomalous U(1) in both the more realistic NAHE-based free fermionic models and those in a general NAHE class. Appearance of an anomalous U(1) in the more realistic NAHE models is shown to be an effect of reduction of world-sheet supersymmetry from (2,2) to (2,0). They show, however, that in more general (2,1) and (2,0) models, all U(1) can remain anomaly-free under certain conditions. Several phenomenological issues related to the anomalous U(1) are discussed. In particular, they note that in some examples the anomalous U(1) arises from the breaking E{sub 6} {yields} SO(10) {times} U(1){sub A}, resulting in U(1){sub A} being family universal.
Date: November 1, 1997
Creator: Cleaver, G.B. & Faraggi, A.E.
Partner: UNT Libraries Government Documents Department