Expansion coefficient of heat kernel of Laplacian operator in Riemann-Cartan space

Kimura, Toshiei

doi:10.1088/0305-4470/14/9/003

Cited by 8 publications

(5 citation statements)

References 4 publications

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“…The calculation of the differential operator spectrum is a mathematical problem with important applications in theoretical physics; it defines the relation between matter fields and quantum corrections to the geometry (for general introduction, see [2,3]). Among various papers that investigate these physical applications, we can cite [4,5,6,7,8,9,10,11,12]. One can mention that the papers [4,5,6,7,8,9,10] consider torsion, which gives the general coupling between geometry and fermions (see also [3] and [13]).…”

Section: Introductionmentioning

confidence: 99%

“…Among various papers that investigate these physical applications, we can cite [4,5,6,7,8,9,10,11,12]. One can mention that the papers [4,5,6,7,8,9,10] consider torsion, which gives the general coupling between geometry and fermions (see also [3] and [13]). The calculation of the determinant of a differential operator corresponding to some particular matter field is a necessary tool to investigate the effective action at the 1-loop level.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Note on the Heat Kernel Method Applied to Fermions

Berredo-Peixoto

2001

Mod. Phys. Lett. A

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The spectrum of the fermionic operators depending on external fields is an important object in quantum field theory. In this paper we prove, using transition to the alternative basis for the γ-matrices, that this spectrum does not depend on the sign of the fermion mass, up to a constant factor. This assumption has been extensively used, but usually without proof. As an illustration, we calculated the coincidence limit of the coefficient a 2 (x, x ′ ) on the general background of metric, vector and axial vector fields.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Note on the Heat Kernel Method Applied to Fermions

Berredo-Peixoto

2001

Mod. Phys. Lett. A

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“…(Except for spin one gauge fields, which are considered to be one-forms and do not couple to torsion.) For details, see [20]- [23] and references therein. Thus, in view of these algebraic inconsistencies concerning higher spin fermions on a Riemann-Cartan background geometry, it does not seem much of a drawback to have additional dynamical inconsistencies arising as a result of the specific choice of the gravitational Lagrangian.…”

Section: Final Remarksmentioning

confidence: 99%

One-parameter teleparallel limit of Poincaré gravity

Leclerc

2005

Phys. Rev. D

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Poincaré gauge theories that, in the absence of spinning matter, reduce to the one-parameter teleparallel theory are investigated with respect to their mathematical consistency and experimental viability. It is argued that the theories can be consistently coupled to the known standard model particles. Moreover, we establish the result that in the classical limit, such theories share a large class of solutions with general relativity, containing, among others, the four classical black hole solutions (Schwarzschild, Reisner-Nordstrøm, Kerr and Kerr-Newman), as well as the complete class of Friedman-Robertson-Walker cosmological solutions, thereby extending older viability results that were restricted to the correct Newtonian limit and to the existence of the Schwarzschild solution.

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“…The general formula for 1-loop counterterms and some of the auxiliary expressions can be found in appendix 2. Note that non-minimal terms (8) and the vacuum term Se,, do not contribute to the 1-loop counterterms. The final expression for 1-loop counterterms has the form:…”

Section: Abelian Gauge Theorymentioning

confidence: 99%

“…It is interesting to note that the traceless and pseudotraceless part of torsion tensor qoPy (3) is not essential from the renormalisation point of view. The terms (8) do not make a contribution to the counterterms at all. Therefore the renormalisation of non-minimal coupling lS never includes other non-minimal parameters.…”

Section: Abelian Gauge Theorymentioning

confidence: 99%

On the renormalisation group equations in curved spacetime with torsion

Buchbinder

Shapiro

1990

Class. Quantum Grav.

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The renormalisation structure of gauge models in curved spacetime with torsion is considered. For Abelian theory the classical action, leading to multiplicatively renormalised theory, is constructed. The multiplicativity of renormalisation requires nonminimal coupling of a vector Abelian field with torsion. The authors investigate the renormalisation group equations for effective nonminimal coupling constants in nonAbelian theory. They find that the equations for essential nonminimal couplings have the universal structure. Due to radiative corrections the interaction between spinor fields and torsion become more intense in the strong gravitational field.

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Expansion coefficient of heat kernel of Laplacian operator in Riemann-Cartan space

Cited by 8 publications

References 4 publications

A Note on the Heat Kernel Method Applied to Fermions

A Note on the Heat Kernel Method Applied to Fermions

One-parameter teleparallel limit of Poincaré gravity

On the renormalisation group equations in curved spacetime with torsion

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