Useful gauges for studying dynamical fermion mass generation in arbitrary space-time dimension

1990 ◽  
Vol 42 (8) ◽  
pp. 2933-2935 ◽  
Author(s):  
Elizabeth H. Simmons
Keyword(s):  
Space Time ◽  
Fermion Mass ◽  
Time Dimension ◽  
Mass Generation ◽  
Arbitrary Space

scholarly journals CURVATURE-INDUCED PHASE TRANSITION IN A FOUR-FERMION THEORY USING THE WEAK CURVATURE EXPANSION

1996 ◽  
Vol 11 (25) ◽  
pp. 4561-4576 ◽  
Author(s):  
TOMOHIRO INAGAKI
Keyword(s):  
Phase Transition ◽  
Chiral Symmetry ◽  
Effective Potential ◽  
Positive Curvature ◽  
Expansion Method ◽  
Space Time ◽  
Fermion Mass ◽  
De Sitter ◽  
Time Dimension ◽  
Arbitrary Space

Curvature–induced phase transition is thoroughly investigated in a four-fermion theory with N components of fermions for arbitrary space–time dimensions (2≤D<4). We adopt the 1/N expansion method and calculate the effective potential for a composite operator [Formula: see text]. The resulting effective potential is expanded asymptotically in terms of the space–time curvature R by using the Riemann normal coordinate. We assume that the space–time curves slowly, and we keep only terms independent of R and terms linear in R. In evaluating the effective potential it is found that first order phase transition is caused and the broken chiral symmetry is restored for a large positive curvature. In the space–time with a negative curvature the chiral symmetry is broken down even if the coupling constant of the four-fermion interaction is sufficiently small. We present the behavior of the dynamically generated fermion mass. The critical curvature, R cr , which divides the symmetric and asymmetric phases, is obtained analytically as a function of the space–time dimension D. At the four-dimensional limit our result R cr agrees with the exact results known in de Sitter space and the Einstein universe.

scholarly journals Hypergeometric presentation for one-loop contributing to H → Z γ

2020 ◽  
Vol 2020 (5) ◽  
Author(s):  
Khiem Hong Phan ◽  
Dzung Tri Tran
Keyword(s):  
Hypergeometric Functions ◽  
Decay Channel ◽  
Form Factors ◽  
Space Time ◽  
Decay Process ◽  
Time Dimension ◽  
Higgs Decay ◽  
Arbitrary Space ◽  
First Time ◽  
Loop Form

Abstract In this paper, new analytic formulas for one-loop contributing to Higgs decay channel $H \rightarrow Z\gamma$ are presented in terms of hypergeometric functions. The calculations are performed by following the technique for tensor one-loop reduction developed in [A. I. Davydychev, Phys. Lett. B 263 (1991) 107]. For the first time, one-loop form factors for the decay process are shown which are valid at arbitrary space–time dimension $d$.

scholarly journals PHASE STRUCTURE OF FOUR-FERMION THEORIES AT FINITE TEMPERATURE AND CHEMICAL POTENTIAL IN ARBITRARY DIMENSIONS

1995 ◽  
Vol 10 (15) ◽  
pp. 2241-2268 ◽  
Author(s):  
T. INAGAKI ◽  
T. KOUNO ◽  
T. MUTA
Keyword(s):  
Phase Transition ◽  
Order Phase Transition ◽  
Phase Structure ◽  
Chemical Potential ◽  
Expansion Method ◽  
Space Time ◽  
Second Order ◽  
Time Dimension ◽  
Arbitrary Space ◽  
Second Order Phase Transition

The phase structure of four-fermion theories is thoroughly investigated with varying temperature and chemical potential for arbitrary space-time dimensions (2≤D<4) by using the 1/N expansion method. It is shown that the chiral symmetry is restored in the theory under consideration for sufficiently high temperature and/or chemical potential. The critical line dividing the symmetric and the broken phase is given explicitly. It is found that for space-time dimension 2≤D<3 both the first order and the second order phase transition occur depending on the value of the temperature and chemical potential while for 3≤D<4 only the second order phase transition exists.

Hypergeometric representation of one-loop Higgs decay to two photons

2019 ◽  
Vol 97 (10) ◽  
pp. 1096-1103 ◽  
Author(s):  
Khiem Hong Phan
Keyword(s):  
Standard Model ◽  
Hypergeometric Function ◽  
Form Factors ◽  
Space Time ◽  
Time Dimension ◽  
Function Representation ◽  
Higgs Decay ◽  
The Standard Model ◽  
Arbitrary Space ◽  
First Time

In this paper, we derive hypergeometric function representation of one-loop contributing to Higgs decay to two photons in the standard model and its extensions. The calculations are performed at general space–time dimension d. For the first time, analytic results are published for form factors that are valid in arbitrary space–time dimension. Moreover, we confirm against analytic results in previous computations that have been available in space–time dimension d = 4 – 2ϵ at ϵ0 expansions.

Dual currents in arbitrary space-time dimension

1976 ◽  
Vol 13 (4) ◽  
pp. 1021-1024
Author(s):  
Edward A. Johnson
Keyword(s):  
Space Time ◽  
Time Dimension ◽  
Arbitrary Space

Unitarity Bound on the Scale of Fermion Mass Generation

1987 ◽  
Vol 59 (21) ◽  
pp. 2405-2407 ◽  
Author(s):  
T. Appelquist ◽  
M. S. Chanowitz
Keyword(s):  
Fermion Mass ◽  
Mass Generation ◽  
Unitarity Bound

scholarly journals POLYHOMOGENEOUS SOLUTIONS OF NONLINEAR WAVE EQUATIONS WITHOUT CORNER CONDITIONS

2006 ◽  
Vol 03 (01) ◽  
pp. 81-141 ◽  
Author(s):  
PIOTR T. CHRUŚCIEL ◽  
SZYMON ŁȨSKI
Keyword(s):  
Initial Data ◽  
Wave Equations ◽  
Space Time ◽  
Einstein Equations ◽  
Nonlinear Wave Equations ◽  
Linear Wave ◽  
Cauchy Problems ◽  
Time Dimension ◽  
Wave Maps ◽  
Corner Conditions

The study of Einstein equations leads naturally to Cauchy problems with initial data on hypersurfaces which closely resemble hyperboloids in Minkowski space-time, and with initial data with polyhomogeneous asymptotics, that is, with asymptotic expansions in terms of powers of ln r and inverse powers of r. Such expansions also arise in the conformal method for analysing wave equations in odd space-time dimension. In recent work it has been shown that for non-linear wave equations, or for wave maps, polyhomogeneous initial data lead to solutions which are also polyhomogeneous provided that an infinite hierarchy of corner conditions holds. In this paper we show that the result is true regardless of corner conditions.

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