scholarly journals Schrödinger representation for a scalar field on curved spacetime

2002 ◽  
Vol 66 (8) ◽  
Author(s):  
Alejandro Corichi ◽  
Jerónimo Cortez ◽  
Hernando Quevedo
Keyword(s):  
Scalar Field ◽  
Curved Spacetime ◽  
Schrödinger Representation

scholarly journals NLO critical exponents of O(N) λ ϕ4 scalar field theories in curved spacetime

2019 ◽  
Vol 28 (01) ◽  
pp. 1950024
Author(s):  
H. A. S. Costa ◽  
P. R. S. Carvalho
Keyword(s):  
Scalar Field ◽  
Critical Exponents ◽  
Conformal Symmetry ◽  
Field Theories ◽  
Quantum Corrections ◽  
Leading Order ◽  
Loop Order ◽  
Curved Spacetime ◽  
Flat Spacetime

In this paper, we investigate analytically the conformal symmetry influence on the next-to-leading order radiative quantum corrections to critical exponents for massless O([Formula: see text]) [Formula: see text] scalar field theories in curved spacetime. We renormalize the theory by applying the Bogoliubov–Parasyuk–Hepp–Zimmermann (BPHZ) method. We find that the critical exponents are the same as that of flat spacetime, at least at the loop order considered. We argue that this result agrees perfectly with the universality hypothesis.

scholarly journals DYNAMICAL BACKREACTION IN ROBERTSON–WALKER SPACETIME

2011 ◽  
Vol 23 (05) ◽  
pp. 531-551 ◽  
Author(s):  
BENJAMIN ELTZNER ◽  
HANNO GOTTSCHALK
Keyword(s):  
Dynamical System ◽  
Scalar Field ◽  
Stress Tensor ◽  
Einstein Equation ◽  
Scale Parameter ◽  
The State ◽  
Curved Spacetime ◽  
Free Scalar ◽  
Hadamard States ◽  
Quantized Field

The treatment of a quantized field in a curved spacetime requires the study of backreaction of the field on the spacetime via the semiclassical Einstein equation. We consider a free scalar field in spatially flat Robertson–Walker spacetime. We require the state of the field to allow for a renormalized semiclassical stress tensor. We calculate the singularities of the stress tensor restricted to equal times in agreement with the usual renormalization prescription for Hadamard states to perform an explicit renormalization. The dynamical system for the Robertson–Walker scale parameter a(t) coupled to the scalar field is finally derived for the case of conformal and also general coupling.

Schrödinger wave functional of a quantum scalar field in static space-times from precanonical quantization

2019 ◽  
Vol 16 (02) ◽  
pp. 1950017 ◽  
Author(s):  
I. V. Kanatchikov
Keyword(s):  
Scalar Field ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Delta Function ◽  
Functional Derivative ◽  
Field Configuration ◽  
Space Time ◽  
Schrödinger Representation ◽  
Limiting Case ◽  
Static Space

The functional Schrödinger representation of a scalar field on an [Formula: see text]-dimensional static space-time background is argued to be a singular limiting case of the hypercomplex quantum theory of the same system obtained by the precanonical quantization based on the space-time symmetric De Donder–Weyl Hamiltonian theory. The functional Schrödinger representation emerges from the precanonical quantization when the ultraviolet parameter [Formula: see text] introduced by precanonical quantization is replaced by [Formula: see text], where [Formula: see text] is the time-like tangent space Dirac matrix and [Formula: see text] is an invariant spatial [Formula: see text]-dimensional Dirac’s delta function whose regularized value at [Formula: see text] is identified with the cutoff of the volume of the momentum space. In this limiting case, the Schrödinger wave functional is expressed as the trace of the product integral of Clifford-algebra-valued precanonical wave functions restricted to a certain field configuration and the canonical functional derivative Schrödinger equation is derived from the manifestly covariant Dirac-like precanonical Schrödinger equation which is independent of a choice of a codimension-one foliation.

scholarly journals Effective Lagrangian for self-interacting scalar field theories in curved spacetime

1993 ◽  
Vol 48 (6) ◽  
pp. 2813-2822 ◽  
Author(s):  
Klaus Kirsten ◽  
Guido Cognola ◽  
Luciano Vanzo
Keyword(s):  
Scalar Field ◽  
Field Theories ◽  
Curved Spacetime ◽  
Effective Lagrangian
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