DIFFERENTIAL RENORMALIZATION FOR CURVED SPACE AND FINITE TEMPERATURE

We derive, based only on simple principles of renormalization in coordinate space, closed renormalized amplitudes and renormalization group constants at one- and two-loop orders for scalar field theories in general backgrounds. This is achieved through a renormalization procedure we develop exploiting the central idea behind differential renormalization, which needs as the only inputs the propagator and the appropriate Laplacian for the backgrounds in question. We work out this coordinate space renormalization in some detail, and subsequently back it up with specific calculations for scalar theories both on curved backgrounds, manifestly preserving diffeomorphism invariance, and at finite temperature.

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Energy–momentum tensors in classical field theories — A modern perspective

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887816400016 ◽

2016 ◽

Vol 13 (08) ◽

pp. 1640001 ◽

Cited By ~ 2

Author(s):

Nicoleta Voicu

Keyword(s):

Geometric Approach ◽

Classical Field ◽

Field Theories ◽

Diffeomorphism Invariance ◽

Type Definition ◽

Classical Field Theories ◽

Opening Up ◽

Hilbert Type ◽

Modern Perspective

The paper presents a general geometric approach to energy–momentum tensors in Lagrangian field theories, based on a global Hilbert-type definition. The approach is consistent with the ones defining energy–momentum tensors in terms of hypermomentum maps given by the diffeomorphism invariance of the Lagrangian — and, in a sense, complementary to these, with the advantage of an increased simplicity of proofs and also, opening up new insights on the topic. A special attention is paid to the particular cases of metric and metric-affine theories.

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Momentum space techniques for curved space–time quantum field theory

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1979.0080 ◽

1979 ◽

Vol 367 (1728) ◽

pp. 123-141 ◽

Cited By ~ 15

Keyword(s):

Field Theory ◽

Quantum Field Theory ◽

Momentum Space ◽

Nuclear Physics ◽

Space Time ◽

Coordinate Space ◽

Quantum Field ◽

Curved Space ◽

Time Quantum ◽

Space Formulation

A momentum space formulation of curved space–time quantum field theory is presented. Such a formulation allows the riches of momentum space calculational techniques already existing in nuclear physics to be exploited in the application of quantum field theory to cosmology and astrophysics. It is demonstrated that one such technique can allow exact, or very accurate approximate, results to be obtained in cases which are intractable in coordinate space. An efficient method of numerical solution is also described.

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DUAL BOSONIC THERMAL GREEN FUNCTION AND FERMION CORRELATORS OF THE MASSIVE THIRRING MODEL AT FINITE TEMPERATURE

Modern Physics Letters A ◽

10.1142/s0217732308024390 ◽

2008 ◽

Vol 23 (10) ◽

pp. 761-767 ◽

Cited By ~ 4

Author(s):

LEONARDO MONDAINI ◽

E. C. MARINO

Keyword(s):

Green Function ◽

Finite Temperature ◽

Thirring Model ◽

Coordinate Space ◽

Massless Scalar ◽

Massless Scalar Field ◽

Infinite Strip ◽

Massive Thirring Model ◽

Series Expression ◽

Upper Half Plane

The Euclidean thermal Green function of the two-dimensional (2D) free massless scalar field in coordinate space is written as the real part of a complex analytic function of a variable that conformally maps the infinite strip -∞ < x < ∞ (0 < τ < β) of the z = x + iτ (τ: imaginary time) plane into the upper-half-plane. Using this fact and the Cauchy–Riemann conditions, we identify the dual thermal Green function as the imaginary part of that function. Using both the thermal Green function and its dual, we obtain an explicit series expression for the fermionic correlation functions of the massive Thirring model (MTM) at a finite temperature.

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Quantum of the bare cosmological constant

Progress of Theoretical and Experimental Physics ◽

10.1093/ptep/ptaa039 ◽

2020 ◽

Vol 2020 (4) ◽

Author(s):

Farhang Loran

Keyword(s):

Scalar Field ◽

Cosmological Constant ◽

Stress Tensor ◽

Parameter Space ◽

Field Theories ◽

Classical Solutions ◽

Curved Spacetimes ◽

Free Scalar ◽

Scalar Theories

Abstract We show that there exist scalar field theories with plausible one-particle states in general $D$-dimensional nonstationary curved spacetimes whose propagating modes are localized on $d\le D$ dimensional hypersurfaces, and the corresponding stress tensor resembles the bare cosmological constant $\lambda_{\rm B}$ in the $D$-dimensional bulk. We show that nontrivial $d=1$ dimensional solutions correspond to $\lambda_{\rm B}< 0$. Considering free scalar theories, we find that for $d=2$ the symmetry of the parameter space of classical solutions corresponding to $\lambda_{\rm B}\neq 0$ is $O(1,1)$, which enhances to $\mathbb{Z}_2\times{\rm Diff}(\mathbb{R}^1)$ at $\lambda_{\rm B}=0$. For $d>2$ we obtain $O(d-1,1)$, $O(d-1)\times {\rm Diff}(\mathbb{R}^1)$, and $O(d-1,1)\times O(d-2)\times {\rm Diff}(\mathbb{R}^1)$ corresponding to, respectively, $\lambda_{\rm B}<0$, $\lambda_{\rm B}=0$, and $\lambda_{\rm B}>0$.

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