Gauge invariance properties of transition amplitudes in gauge theories. I

The functional approach developed earlier for scattering theory in quantum field theory makes it possible to make an explicit and complete study of the gauge invariance properties oftransition amplitudes (not just of the gauge transformations of Green's functions) in covariant and noncovariant gauges. This paper is devoted to the Abelian gauge theory of quantum electrodynamics. Using the powerful technique of functional differentiation and starting from the Coulomb gauge, the gauge invariance property of transition amplitudes,up to gauge-dependent scaling factors, isexplicitly established in arbitrary gauges. The key ingredients in the analysis are the derived exact expression for the vacuum-to-vacuum transition amplitude, introducing in the process arbitrary gauges, and the idea of stimulated emissions by external sources studied earlier.     

Pump pulse duration dependence of coherent phonon amplitudes in antimony

Coherent optical phonons of A_1k and E_k symmetry in antimony have been studied using the femtosecond pump–probe technique. By varying the pump-pulse duration and keeping the probe duration constant, it was shown that the amplitude of coherent phonons of both symmetries exponentially decreases with increasing pulse width. It was found that the amplitude decay rate for the fully symmetric phonons with larger frequency is greater than that of the doubly degenerate phonons, whereas the frequency and lifetime for coherent phonons of both symmetries do not depend on the pump-pulse duration. Based on this data, the possibility of separation between dynamic and kinematic contributions to the generation mechanism of coherent phonons is discussed.     

Gauge dependence of the effective action in multidimensional supergravities

The problem of gauge dependence of the effective action in multidimensional supergravities (SG) is investigated. As an example d=5 SGs are considered. The convenient gauge-dependent effective action (EA) and gauge-invariant Vilkovisky-De Witt EA in d=5, N=2, 4, 6, 8 SGs on the background R₄×S₁ with accuracy to linear curvature terms are obtained. The convenient three-gauge-parameter-dependent EA in d=5, N=2 gauged SG on the background R₄×S₁ is calculated. The Vilkovisky-De Witt EA in d=5 SGs on the background R₄×S₁ at non-zero temperature is also obtained.     

Gauge dependence of ultraviolet behavior of gauge theories

The gauge dependence of ultraviolet behavior of gauge theories is examined on the basis of renormalization-group equation. Non-Abelian gauge theories are confirmed to be asymptotically free in an arbitrary gauge. It is also shown that the effective gauge parameter approaches a finite value in the ultraviolet limit in contrast with the case of QED.     

Gauge dependence of effective potential and self-consistent dimensional reduction

The gauge dependence of the effective potential determining the Kaluza-Klein radius self-consistently is contrasted to that belonging to a gauge theory with spontaneous symmetry breaking at finite temperature. Formally the two quantities are computed in the same way and obey the same Ward identities, but a gauge-independent approximation scheme is possible only in the latter case because of the coupling between the Goldstone field and the longitudinal vector field. The connection to the Ward identities of the two theories is also obtained.     

Gauge dependence of renormalization group parameters in ghost-free non-abelian gauge theories

We discuss the gauge dependence of the renormalization group parameters in a class of ghost-free non-abelian gauge theories. We show, using the n-dimensional regularization with the “minimal” renormalization procedure, that these parameters are gauge independent.     

Gauge and scheme dependence of threshold effects in spontaneously broken theories

An enormous discrepancy between the running coupling constants obtained in twostandard renormalization schemes is found within broken scalar QED. One of these renormalization schemes is shown to be manifestly gauge independent, whereas the other turns out to be highly gauge dependent. Although these findings apply to the abelian case, they provide a guidance for the nonabelian case as well.     

Gauge dependence of the effective action in multidimensional theories of supergravity

Using the 5-dimensional supergravity as an example, the problem of gauge dependence of the effective action (EA) of multidimensional SUGRA's is discussed. The standard and the Vikovisky-De Witt EA's are computed up to the terms linear in curvature for d=5, N=2, 4, 6, 8 SUGRA's on the R₄,×S₁ background, where R₄, is a 4-dimensional curved space, and S₁ a 1-dimensional sphere. The standard EA obtained in d=5, N= 2 gauge SUGRA on the R ₄ ⁰ ×S₁, where R ₄ ⁰ is a flat 4-dimensional space, depends on three gauge parameters. The gauge-invariant Vilkovsky-De Witt EA is computed for a d=5 SUGRA with broken symmetry on the r ₄ ⁰ ×S₁ background, where R ₄ ⁰ is a 4-dimensional space with nonzero temperature.Translated from Izvestiya Vyssihkh Uchebnykh Zavedenii, Fizika, No. 5, pp. 53–59, May, 1989.I am grateful to I. L. Bukhbinder, I. V. Tyutin, and A. A. Tseitlin for many useful discussions.     

Gauge dependence of Green’s functions in QCD and QED

When all Green’s functions are known in a given gauge we may raise the question of whether it is possible or not to derive the corresponding ones in a different gauge. The answer is negative in QCD but affirmative in QED provided that we confine ourselves to the covariant gauge characterized by a gauge parameter α. We shall discuss the physical significance of this conclusion.     

Gauge dependence of gravitational correction to running of gauge couplings

Recently an interesting idea has been put forward by Robinson and Wilczek that the incorporation of quantized gravity in the framework of Abelian and non-Abelian gauge theories results in a correction to the running of gauge coupling and, as a consequence, increase the grand unification scale and asymptotic freedom. In this Letter it is shown by explicit calculations that this correction depends on the choice of gauge.     

MBPT studies of van der Waals molecules

The many-body perturbation theory is employed for the calculation of the interaction potential for the F^- … He system in the framework of the supermolecule method. A particular attention is paid to the choice of the basis set functions for the two subsystems and the related basis set superposition effects. It has been found that the main features of the interaction potential are recovered in the SCF approximation. The SCF potential has its minimum at the distance R = 6·4 a ₀ with the interaction energy of 53 cm^-1. The complete fourth-order MBPT method gives the potential minimum position and depth equal to 6·5 a ₀ and 64 cm^-1, respectively. The basis set superposition effects estimated by using the counterpoise technique are negligibly small for the SCF interaction potential, while at the correlated level their magnitude is comparable to the value of the total correlation contribution to the interaction energy. The basis set superposition effect in calculations of the electron correlation contribution to weak intermolecular interactions is found to be the major factor limiting the reliability of the corresponding theoretical data.     

Gauge dependence of world lines and invariance of theS-matrix in relativistic classical mechanics

The notion of world lines is studied in the constraint Hamiltonian formulation of relativistic point particle dynamics. The particle world lines are shown to depend in general (in the presence of interaction) on the choice of the equal-time hyperplane (the only exception being the elastic scattering of rigid balls). However, the relative motion of a two-particle system and the (classical)S-matrix are independent of this choice.A preliminary version of this paper was circulated as ICTP, Trieste, Internal Report IC/79/59On leave of absence from Institute of Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, Sofia 1184, Bulgaria     

Corrections to VMD in the photoproduction of vector mesons I: Mass dependence of amplitudes

We study the dependence of the vector meson scattering amplitudes on the external masses, assuming that the most important effects arise from the coupling of the vector mesons to low mass intermediate states which mediate the scattering. The consequence is that the amplitudes for ?⁰ and ø photoproduction are modified by approximately + 10% and ?15% respectively. This result is equivalent to naively using the coupling constants from the e⁺e^- decay widths and ignoring the mass variation effects. The analysis also calls attention to residual uncertainties at the several percent level.