On the consistency of self-consistent dimensional reduction

1986 ◽  
Vol 64 (5) ◽  
pp. 641-643 ◽  
Author(s):  
G. Kunstatter ◽  
D. J. Toms
Keyword(s):  
Dimensional Reduction ◽  
Gauge Coupling ◽  
Coupling Constant ◽  
Gauge Dependence ◽  
Loop Approximation ◽  
Self Consistent ◽  
Klein Theory ◽  
The One ◽  
Self Consistency ◽  
Kaluza Klein

Several aspects of self-consistent dimensional reduction in Kaluza–Klein theory are addressed. First, the validity of the one-loop approximation in quantum gravity with a cosmological constant is discussed. Second, a distinction is made between mathematical self-consistency and physical self-consistency. Finally, the possible gauge dependence of the physical predictions for the radius and gauge coupling constant is analyzed within the context of recent theorems concerning the gauge invariance of the one-loop gravitational effective action.

The importance of quantum effects in Kaluza–Klein theory

1986 ◽  
Vol 64 (5) ◽  
pp. 644-652 ◽  
Author(s):  
D. J. Toms
Keyword(s):  
Effective Action ◽  
Gauge Coupling ◽  
Quantum Effects ◽  
Induced Gravity ◽  
Yang Mills ◽  
Self Consistent ◽  
Klein Theory ◽  
Dimensional Gravity ◽  
The Stability ◽  
Kaluza Klein

This paper presents a discussion of the role of quantum effects in Kaluza–Klein theories. It is demonstrated why it is not possible to examine the existence of self-consistent solutions induced by quantum corrections to the classical theory if only the vacuum energy is used. The importance of the induced gravity and induced Yang–Mills terms in the effective action are emphasized. General criteria are given for the existence of self-consistent solutions in certain cases, and an expression is given for the gauge-coupling constant. Quantization of five-dimensional gravity with a cosmological constant is considered. Expressions are given for the constants that multiply the induced gravity and Yang–Mills terms in the one-loop effective action for this theory. Although the theory is one-loop finite, the necessity for performing finite renormalizations—a fact that has hitherto been overlooked—is discussed. Results of an analysis of the stability of self-consistent solutions are given, where it is shown why many of the solutions are unstable to small perturbations. A number of prospects for future work are given.

scholarly journals Prediction of Weinberg Angle in Discretized Kaluza-Klein Theory

2019 ◽  
Vol 35 (3) ◽  
Author(s):  
Nguyen Van Dat
Keyword(s):  
Coupling Constant ◽  
New Approach ◽  
Electron Positron ◽  
The Standard Model ◽  
Single Coupling ◽  
Klein Theory ◽  
Weinberg Angle ◽  
The One ◽  
Collider Experiment ◽  
Kaluza Klein

In Discretized Kaluza-Klein theory (DKKT) the gauge fields emerge as components of gravity with a single coupling constant. Therefore, it provide a new approach to fix the parameters of the Standard Model, and in particular the Weinberg angle. We show that in our approach using DKKT, the predicted value of Weinberg angle is exactly the one measured in the electron-positron collider experiment at Q = 91.2 GeV/c. The result is compared with the one predicted the group theoretic methods.

AN IMPROVED ONE-LOOP ANALYSIS OF THE λϕ4 THEORY AT FINITE TEMPERATURE

1987 ◽  
Vol 02 (03) ◽  
pp. 713-728 ◽  
Author(s):  
SWEE-PING CHIA
Keyword(s):  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Zero Temperature ◽  
Coupling Constant ◽  
Loop Analysis ◽  
Temperature Dependent ◽  
Effective Coupling ◽  
Loop Approximation ◽  
The One ◽  
Dependent Mass

The λϕ4 theory with tachyonic mass is analyzed at T ≠ 0 using an improved one-loop approximation in which each of the bare propagators in the one-loop diagram is replaced by a dressed propagator to take into account the higher loop effects. The dressed propagator is characterized by a temperature-dependent mass which is determined by a self-consistent relation. Renomalization is found to be necessarily temperature-dependent. Real effective potential is obtained, giving rise to real effective mass and real coupling constant. For T < Tc, this is achieved by first shifting the ϕ field by its zero-temperature vacuum expectation value. The effective coupling constant is found to exhibit the striking behavior that it approaches a constant nonzero value as T → ∞.

A HAMILTONIAN TREATMENT OF FIVE-DIMENSIONAL KALUZA–KLEIN GRAVITY

2000 ◽  
Vol 09 (04) ◽  
pp. 445-458 ◽  
Author(s):  
W. N. SAJKO
Keyword(s):  
Total Mass ◽  
Soliton Solutions ◽  
Schwarzschild Solution ◽  
Coordinate Dependence ◽  
Klein Theory ◽  
The One ◽  
Induced Matter ◽  
Classical Derivation ◽  
Area Law ◽  
Kaluza Klein

We give a Hamiltonian treatment of 5D vacuum Kaluza–Klein theory that is unrestricted in the extra coordinate dependence. When the extra coordinate dependence is removed from the 5D metric we recover the Hamiltonian for gravity and electromagetism nonminimally coupled to a scalar field. The energies of 5D uncharged and charged soliton solutions are calculated via the Hamiltonian and are identified with the total mass. The expressions for the total mass are shown to agree with the sum of scalar and gravitational masses calculated from the scalar-tensor induced matter in 4D. A semi-classical derivation of the temperature for the uncharged solitons is calculated and it is shown that the only nontrivial member of the 5D class is the 4D Schwarzschild solution trivially embedded in 5D, and therefore the entropy obeys the one-quarter area law.

Self-Consistent Hole Motion and Spin Excitations in A Quantum Antiferromagnet

1989 ◽  
Vol 03 (12) ◽  
pp. 1913-1932 ◽  
Author(s):  
Z.B. Su ◽  
Y.M. Li ◽  
W.Y. Lai ◽  
L. Yu
Keyword(s):  
The Self ◽  
Spin Excitation ◽  
Spin Correlations ◽  
Local Distortion ◽  
Spin Excitations ◽  
Self Consistent ◽  
The Stability ◽  
The One ◽  
Quantum Antiferromagnet ◽  
Self Consistency

A new quantum Bogoliubov-de Gennes (BdeG) formalism is developed to study the self-consistent motion of holes and spin excitations in a quantum antiferromagnet within the generalized t-J model. On the one hand, the effects of local distortion of spin configurations and the renormalization of the hole motion due to virtual excitations of the distorted spin background are treated on an equal footing to obtain the hole wave function and its spectrum, as well as the effective mass for a propagating hole. On the other hand, the change of the spin excitation spectrum and the spin correlations due to the presence of dynamical holes are studied within the same adiabatic approximation. The stability of the hole states with respect to such changes justifies the self-consistency of the proposed formalism.

scholarly journals FIVE-DIMENSIONAL KALUZA–KLEIN THEORY WITH A SOURCE

2004 ◽  
Vol 19 (29) ◽  
pp. 5043-5050 ◽  
Author(s):  
YONGGE MA ◽  
JUN WU
Keyword(s):  
Electromagnetic Field ◽  
Test Particle ◽  
Dimensional Reduction ◽  
Dimensional Space ◽  
Space Time ◽  
Fifth Dimension ◽  
Klein Theory ◽  
Dimensional Space Time ◽  
Kaluza Klein

A free test particle in five-dimensional Kaluza–Klein space–time will show its electricity in the reduced four-dimensional space–time when it moves along the fifth dimension. In the light of this observation, we study the coupling of a five-dimensional dust field with the Kaluza–Klein gravity. It turns out that the dust field can curve the five-dimensional space–time in such a way that it provides exactly the source of the electromagnetic field in the four-dimensional space–time after the dimensional reduction.

scholarly journals COMPLETE CLASSES OF GUTS WITH VANISHING ONE-LOOP BETA FUNCTIONS

1994 ◽  
Vol 09 (29) ◽  
pp. 5053-5075
Author(s):  
WOLFGANG LUCHA ◽  
FRANZ F. SCHÖBERL
Keyword(s):  
Gauge Coupling ◽  
Coupling Constants ◽  
Coupling Constant ◽  
Finiteness Conditions ◽  
Grand Unified Theories ◽  
Unified Theories ◽  
Dimensionless Coupling ◽  
The One ◽  
The Masses ◽  
Gauge Coupling Constant

By explicit solution of the one-loop finiteness conditions for all dimensionless coupling constants (i.e. the gauge coupling constant as well as Yukawa and quartic scalar-boson self-interaction coupling constants), two classes of grand unified theories characterized by renormalization-group beta functions which all vanish at least at the one-loop level are constructed and analyzed with respect to the (suspected) appearance of quadratic divergences, with the result that without exception in all of these models the masses of both vector and scalar bosons receive quadratically divergent one-loop contributions.

scholarly journals ELEMENTARY PARTICLE INTERACTION FROM A KALUZA-KLEIN SCHEME

2008 ◽  
Vol 23 (08) ◽  
pp. 1182-1189
Author(s):  
FRANCESCO CIANFRANI ◽  
GIOVANNI MONTANI
Keyword(s):  
Elementary Particle ◽  
Dimensional Reduction ◽  
Dimensional Space ◽  
Particle Interaction ◽  
Gauge Coupling ◽  
Space Time ◽  
Reduction Procedure ◽  
Weak Model ◽  
Dimensional Space Time ◽  
Kaluza Klein

We discuss properties of particles and fields in a multi-dimensional space-time, where the geometrization of gauge interactions can be performed. As far as spinors are concerned, we outline how the gauge coupling can be recognized by a proper dependence on extra-coordinates and by the dimensional reduction procedure. Finally applications to the Electro-Weak model are presented.

scholarly journals HIGGS MASS IN THE STANDARD MODEL FROM COUPLING CONSTANT REDUCTION

2002 ◽  
Vol 17 (03) ◽  
pp. 335-346 ◽  
Author(s):  
B. ANANTHANARAYAN ◽  
J. PASUPATHY
Keyword(s):  
Renormalization Group ◽  
Standard Model ◽  
Top Quark ◽  
Higgs Mass ◽  
Gauge Coupling ◽  
Renormalization Scale ◽  
Coupling Constant ◽  
Top Quark Mass ◽  
The Standard Model ◽  
The One

Plausible interrelations between parameters of the standard model are studied. The empirical value of the top quark mass, when used in the renormalization group equations, suggests that the ratio of the color SU(3) gauge coupling g3, and the top coupling gt is independent of the renormalization scale. On the other hand, the variety of top-condensate models suggests that the Higgs self-coupling λ is proportional to [Formula: see text]. Invoking the requirement that the ratio [Formula: see text] is independent of the renormalization scale t, fixes the Higgs mass. The pole mass of the Higgs (which differs from the renormalization group mass by a few percent) is found to be ~ 154 GeV for the one-loop equations and ~ 148 GeV for the two-loop equations.

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