On the effective Lagrangian for scalar electrodynamics

1985 ◽  
Vol 63 (3) ◽  
pp. 431-434 ◽  
Author(s):  
Abul Mansur Chowdhury ◽  
Gerry McKeon
Keyword(s):  
Electromagnetic Field ◽  
Electromagnetic Fields ◽  
Vector Fields ◽  
Quantum Fluctuations ◽  
External Electromagnetic Field ◽  
Second Order ◽  
Type Approximation ◽  
Effective Lagrangian ◽  
Scalar And Vector Fields ◽  
The One

The one-loop effective Lagrangian in scalar electrodynamics is computed using an expansion to second order in the external electromagnetic field and a WKB-type approximation. Quantum fluctuations of both the scalar and vector fields about background scalar and electromagnetic fields are considered.

scholarly journals ONE-LOOP EFFECTIVE POTENTIAL FOR SCALAR AND VECTOR FIELDS ON HIGHER-DIMENSIONAL NONCOMMUTATIVE FLAT MANIFOLDS

2001 ◽  
Vol 16 (23) ◽  
pp. 1479-1486 ◽  
Author(s):  
A. A. BYTSENKO ◽  
A. E. GONÇALVES ◽  
S. ZERBINI
Keyword(s):  
Zeta Function ◽  
Vector Fields ◽  
Dimensional Regularization ◽  
Massless Scalar ◽  
Quantum Field Theories ◽  
Dimensional Manifold ◽  
Logarithmic Term ◽  
Scalar And Vector Fields ◽  
The One ◽  
Flat Manifolds

The non-planar contribution to the effective potentials for massless scalar and vector quantum field theories on D-dimensional manifold with p compact noncommutative extra dimensions is evaluated by means of dimensional regularization implemented by zeta function techniques. It is found that, the zeta function associated with the one-loop operator may not be regular at the origin. Thus, the related heat kernel trace has a logarithmic term in the short t asymptotic expansion. Consequences of this fact are briefly discussed.

scholarly journals Derivative expansion for the one-loop effective Lagrangian in QED

1996 ◽  
Vol 74 (5-6) ◽  
pp. 282-289 ◽  
Author(s):  
V. P. Gusynin ◽  
I. A. Shovkovy
Keyword(s):  
Electromagnetic Field ◽  
Field Strength ◽  
External Field ◽  
Explicit Expression ◽  
Derivative Expansion ◽  
Effective Lagrangian ◽  
Constant Electromagnetic Field ◽  
The One ◽  
Derivatives Of

The derivative expansion of the one-loop effective Lagrangian in QED4 is considered. The first term in such an expansion is the famous Schwinger result for a constant electromagnetic field. In this paper we give an explicit expression for the next term containing two derivatives of the field strength Fμν. The results are presented for both fermion and scalar electrodynamics. Some possible applications of an inhomogeneous external field are pointed out.

Singularities of electron kernel functions in an external electromagnetic field

1954 ◽  
Vol 222 (1148) ◽  
pp. 93-108 ◽  
Keyword(s):  
Electromagnetic Field ◽  
Perturbation Theory ◽  
Wave Equation ◽  
Vacuum Polarization ◽  
Proper Time ◽  
External Electromagnetic Field ◽  
Kernel Functions ◽  
Second Order ◽  
Significant Part ◽  
Second Order Wave Equation

The electron kernel functions are derived from solutions of the second-order wave equation, using the proper-time parametrization. Iterated kernel functions are introduced and a gauge-independent perturbation theory is developed. The separation of singular parts proceeds in terms of the iterated kernel functions valid in the absence of an electromagnetic field, and the singular expressions which have to be compensated in order to determine the physically significant part of the vacuum polarization are obtained in a more transparent form than those given originally by Heisenberg.

FERMIONIC SUPERCONDUCTIVITY IN THE DENSE WEINBERG-SALAM MODEL

1990 ◽  
Vol 05 (17) ◽  
pp. 3417-3448 ◽  
Author(s):  
E.J. FERRER ◽  
V. DE LA INCERA ◽  
A.E. SHABAD
Keyword(s):  
Electromagnetic Field ◽  
Penetration Depth ◽  
Energy Gap ◽  
Polarization Operator ◽  
External Electromagnetic Field ◽  
Condensate Phase ◽  
Fermion Loop ◽  
Zero Momentum ◽  
The One

The superconducting behavior of the W-condensate phase of the Weinberg-Salam liquid is investigated. The removal of the W-orientation degeneracy by a small external electromagnetic field imposed on the W-condensate is found. Against the background of the condensed W-mesons the left-lepton spectrum undergoes a restructuring with the appearance of an energy gap between all the particle-antiparticle states, and the joining of particles and antiparticles in the new spectrum. Some of these peculiarities are indicated as a signal of the electrical superconductivity of such a medium. The definitive conclusions about the fermion superconductivity are achieved by studying the contribution to the London’s equation of the one-fermion loop polarization operator against the W-condensate background at zero momentum. The London’s penetration depth λ L is found in the limit of small W-condensate amplitude.

scholarly journals ANALYTIC RESULTS FOR THE EFFECTIVE ACTION

1991 ◽  
Vol 06 (30) ◽  
pp. 5409-5433 ◽  
Author(s):  
STEVEN K. BLAU ◽  
MATT VISSER ◽  
ANDREAS WIPF
Keyword(s):  
Electromagnetic Field ◽  
Asymptotic Expansion ◽  
Zeta Function ◽  
Effective Action ◽  
Strong Field ◽  
Weak Field ◽  
Four Dimensions ◽  
Effective Lagrangian ◽  
Constant Electromagnetic Field ◽  
The One

Motivated by the seminal work of Schwinger, we obtain explicit closed-form expressions for the one-loop effective action in a constant electromagnetic field. We discuss both massive and massless charged scalars and spinors in two, three and four dimensions. Both strong-field and weak-field limits are calculable. The latter limit results in an asymptotic expansion whose first term reproduces the Euler-Heinsenberg effective Lagrangian. We use the prescription of zeta-function renormalization, and indicate its relationship to Schwinger’s renormalized effective action.

scholarly journals THE FINITE VACUUM ENERGY FOR SPINOR, SCALAR AND VECTOR FIELDS

1995 ◽  
Vol 10 (16) ◽  
pp. 2333-2347
Author(s):  
N.N. SHTYKOV
Keyword(s):  
Physical Model ◽  
Vector Fields ◽  
Vacuum Energy ◽  
Scalar Fields ◽  
Casimir Energy ◽  
Divergent Part ◽  
Scalar And Vector Fields ◽  
Massive Spinor ◽  
The One

We compute the one-loop potential (the Casimir energy) for scalar fields with coupling ξR and massive spinor and vector fields on the spaces Rm+1×Y with Y=SN, CP2. We find that in most of the models a divergent part of the Casimir energy on even-dimensional spaces is canceled by means of the appropriate values of ξ, msp, mv. As a physical model we consider spinor electrodynamics on four-dimensional product manifolds and show that the Casimir energy is finite on R1×S3, R3×S1 and R2×S2 for msp=0, msp=0 and [Formula: see text] respectively.

scholarly journals Large N external-field quantum electrodynamics

2022 ◽  
Vol 2022 (1) ◽  
Author(s):  
Felix Karbstein
Keyword(s):  
Electromagnetic Field ◽  
External Field ◽  
Effective Action ◽  
Quantum Electrodynamics ◽  
Strong Field ◽  
Loop Order ◽  
Field Limit ◽  
Effective Lagrangian ◽  
Large N ◽  
The One

Abstract We advocate the study of external-field quantum electrodynamics with N charged particle flavors. Our main focus is on the Heisenberg-Euler effective action for this theory in the large N limit which receives contributions from all loop orders. The contributions beyond one loop stem from one-particle reducible diagrams. We show that specifically in constant electromagnetic fields the latter are generated by the one-loop Heisenberg-Euler effective Lagrangian. Hence, in this case the large N Heisenberg-Euler effective action can be determined explicitly at any desired loop order. We demonstrate that further analytical insights are possible for electric-and magnetic-like field configurations characterized by the vanishing of one of the secular invariants of the electromagnetic field and work out the all-orders strong field limit of the theory.

scholarly journals On Tubes of Force in a special class of electromagnetic fields

1922 ◽  
Vol 41 ◽  
pp. 100-107
Author(s):  
G. S. Eastwood
Keyword(s):  
Electromagnetic Field ◽  
Electromagnetic Fields ◽  
Electromagnetic Force ◽  
Special Class ◽  
Royal Society ◽  
Space Time ◽  
The Other ◽  
Family Meeting ◽  
The One

Professor Whittaker, in a paper entitled “On Tubes of Electromagnetic Force” {see Proceedings of the Royal Society of Edinburgh, Vol. XLII., Part I. (No 1)}, introduces certain surfaces, which he names calamoids, in connection with an electromagnetic field in the four-dimensional world of space-time. The calamoids consist of “a convariant family of surfaces which when the field is purely electrostatic or purely magnetostatic reduce to the ordinary Faraday tubes of force.” Professor Whittaker, in the paper referred to, also introduces two sets of surfaces, each a covariant family of ∞2 surfaces, one of them named the electropotential surfaces, and the other family the magnetopotential surfaces of the electromagnetic field. The electropotential surfaces and the magnetopotential surfaces are shown to be everywhere absolutely orthogonal. (One member of each family meeting at a point, any line from this point in the one family is orthogonal to every line through the point in the other family). Moreover, a “calamoid, at every one of its points, is half-parallel and half-orthogonal to the electropotential surface which passes through the point, and is also half-parallel and half-orthogonal to the magnetopotential surface which passes through the point.”

scholarly journals Electromagnetic field vulnerability of complex systems – an application of EM topology

2008 ◽  
Vol 6 ◽  
pp. 273-277 ◽  
Author(s):  
R. Kanyou Nana ◽  
S. Dickmann ◽  
F. Sabath
Keyword(s):  
Electromagnetic Field ◽  
Complex Systems ◽  
Electromagnetic Fields ◽  
Hybrid Method ◽  
External Electromagnetic Field ◽  
Initial Problem ◽  
Electronic Equipment ◽  
Simplified Model ◽  
Coupling Mechanisms

Abstract. In complex systems like ships or airplanes many tasks vital to the function of the system are executed by electronic equipment. Earlier research Camp (2004) – Nitsch (2005) has shown that there are frequency ranges in many of these systems, in which disturbances in the system will be observed if an external electromagnetic field exceeds a certain amplitude limit. On the basis of a simplified model in which the dominating coupling mechanisms in complex systems are shown, we will present a method which allows to analyze the vulnerability to electromagnetic fields. The method is based on the segmentation of the initial problem into subproblems with respect to the coupling mechanisms. Under the assumption that the obtained classes can be handled separately, the subproblems are solved and superposed to the overall solution. The Electromagnetic Topology Baum (1982) – Lee (1982) is used to solve the subproblems. This leads to a hybrid method combining different solution approaches. The subproblems are decomposed into smaller subproblems with respect to the shielding levels. This procedure allows us to determine the coupled disturbances into the system. Finally the solution is verified with respect to prescripted limits.

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