Relation between the solitons of Yang–Mills–Higgs fields in 2+1 dimensional Minkowski space–time and anti-de Sitter space–time

In recent papers,1,2 it has been shown that the presence of negative norm states or negative frequency solutions are indispensable for a fully covariant quantization of the minimally coupled scalar field in de Sitter space. Their presence, while leaving unchanged the physical content of the theory, offers the advantage of eliminating any ultraviolet divergence in the vacuum energy2 and infrared divergence in the two point function.3 We attempt here to extend this method to the interacting quantum field in Minkowski space-time. As an illustration of the procedure, we consider the λϕ4 theory in Minkowski space-time. The mathematical consequences of this method is the disappearance of the ultraviolet divergence to the one-loop approximation. This means, the effect of these auxiliary negative norm states is to allow an automatic renormalization of the theory in this approximation.

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A STRING MODEL FOR D-DIMENSIONAL DE SITTER SPACE–TIME AND EQUATIONS OF MOTION

International Journal of Modern Physics A ◽

10.1142/s0217751x0502553x ◽

2005 ◽

Vol 20 (26) ◽

pp. 6065-6081

Author(s):

PAUL BRACKEN

Keyword(s):

Evolution Equations ◽

Gordon Equation ◽

Equations Of Motion ◽

String Model ◽

De Sitter Space ◽

Space Time ◽

System Of Equations ◽

De Sitter ◽

Minkowski Space Time ◽

Dimensional Minkowski Space

De Sitter space–time is considered to be represented by a D-dimensional hyperboloid embedded in (D+1)-dimensional Minkowski space–time. The string equation is derived from a string action which contains a Lagrange multiplier to restrict coordinates to de Sitter space–time. The string system of equations is equivalent to a type of generalized sinh–Gordon equation. The evolution equations for all the variables including the coordinates and their derivatives are obtained for D=2,3 and 4.

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(N, p, q) HARMONIC SUPERSPACE

International Journal of Modern Physics A ◽

10.1142/s0217751x95001820 ◽

1995 ◽

Vol 10 (27) ◽

pp. 3901-3919 ◽

Cited By ~ 98

Author(s):

G.G. HARTWELL ◽

P.S. HOWE

Keyword(s):

Minkowski Space ◽

Space Time ◽

Harmonic Superspace ◽

Curved Space ◽

Yang Mills ◽

Invariant Integrals ◽

Minkowski Space Time ◽

Dimensional Minkowski Space ◽

Harmonic Superspaces ◽

Super Yang Mills Theory

A family of harmonic superspaces associated with four-dimensional Minkowski space-time is described. Applications are made to free massless supermultiplets, invariant integrals and super-Yang-Mills theory. Generalization to curved space-times is performed, with emphasis on conformal supergravities.

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LIFETIME OF A DE SITTER PARTICLE

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887808003296 ◽

2008 ◽

Vol 05 (08) ◽

pp. 1243-1254

Author(s):

HENRI EPSTEIN

Keyword(s):

Perturbation Theory ◽

Minkowski Space ◽

Principal Series ◽

De Sitter Space ◽

Space Time ◽

De Sitter ◽

Complementary Series ◽

First Order ◽

Interaction Terms ◽

Minkowski Space Time

The familiar rule which, in Minkowski space-time, forbids the decay of a particle into heavier products, does not hold in de Sitter space-time. We study, in first order of perturbation theory, the decay of a particle of the "principal series" and show that it may decay into two particles of any of the "principal" or "complementary" series (with suitable interaction terms). Spectral conditions reappear in the decay of a "complementary" particle: but its lifetime is 0.

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A MAXWELL-LIKE FORMULATION OF GRAVITATIONAL THEORY IN MINKOWSKI SPACE–TIME

International Journal of Modern Physics D ◽

10.1142/s0218271807010547 ◽

2007 ◽

Vol 16 (06) ◽

pp. 1027-1041 ◽

Cited By ~ 8

Author(s):

EDUARDO A. NOTTE-CUELLO ◽

WALDYR A. RODRIGUES

Keyword(s):

Gravitational Field ◽

Minkowski Space ◽

Gravitational Theory ◽

Space Time ◽

Lorentzian Geometry ◽

Field Equations ◽

Yang Mills ◽

Minkowski Space Time ◽

Clifford Bundle ◽

Gauge Fixing

Using the Clifford bundle formalism, a Lagrangian theory of the Yang–Mills type (with a gauge fixing term and an auto interacting term) for the gravitational field in Minkowski space–time is presented. It is shown how two simple hypotheses permit the interpretation of the formalism in terms of effective Lorentzian or teleparallel geometries. In the case of a Lorentzian geometry interpretation of the theory, the field equations are shown to be equivalent to Einstein's equations.

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Elastic shocks in relativistic rigid rods and balls

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2018.0858 ◽

2019 ◽

Vol 475 (2225) ◽

pp. 20180858 ◽

Cited By ~ 1

Author(s):

João L. Costa ◽

José Natário

Keyword(s):

Free Boundary ◽

Minkowski Space ◽

Initial Conditions ◽

Equations Of Motion ◽

Time Derivative ◽

Space Time ◽

Spherically Symmetric ◽

Soft Phase ◽

Minkowski Space Time ◽

Dimensional Minkowski Space

We study the free boundary problem for the ‘hard phase’ material introduced by Christodoulou in (Christodoulou 1995 Arch. Ration. Mech. Anal. 130 , 343–400), both for rods in (1 + 1)-dimensional Minkowski space–time and for spherically symmetric balls in (3 + 1)-dimensional Minkowski space–time. Unlike Christodoulou, we do not consider a ‘soft phase’, and so we regard this material as an elastic medium, capable of both compression and stretching. We prove that shocks must be null hypersurfaces, and derive the conditions to be satisfied at a free boundary. We solve the equations of motion of the rods explicitly, and we prove existence of solutions to the equations of motion of the spherically symmetric balls for an arbitrarily long (but finite) time, given initial conditions sufficiently close to those for the relaxed ball at rest. In both cases we find that the solutions contain shocks if and only if the pressure or its time derivative do not vanish at the free boundary initially. These shocks interact with the free boundary, causing it to lose regularity.

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