scholarly journals A NATURAL RENORMALIZATION OF THE ONE-LOOP EFFECTIVE ACTION FOR SCALAR FIELD IN CURVED SPACETIME

2005 ◽  
Vol 14 (02) ◽  
pp. 219-223 ◽  
Author(s):  
MOHAMMAD VAHID TAKOOK
Keyword(s):  
Scalar Field ◽  
Effective Action ◽  
Minkowski Spacetime ◽  
De Sitter ◽  
Renormalization Procedure ◽  
Negative Norm ◽  
Curved Space ◽  
Loop Approximation ◽  
The One ◽  
Infrared Divergences

It has been shown that the negative norm states necessarily appear in a covariant quantization of the free minimally coupled scalar field in de Sitter space.1,2 In this process, ultraviolet and infrared divergences have been automatically eliminated.3 A natural renormalization of the one-loop interacting quantum field in Minkowski spacetime (λϕ4 theory) has been achieved through the consideration of the negative norm states.4 The one-loop effective action for scalar field in a general curved space-time has been calculated by this method, and a natural renormalization procedure in the one-loop approximation has been established.

ONE-LOOP FINITE TEMPERATURE EFFECTIVE ACTION FOR COMPOSITE FIELDS IN CURVED SPACE

1995 ◽  
Vol 10 (03) ◽  
pp. 389-420
Author(s):  
J. BALAKRISHNAN
Keyword(s):  
Effective Action ◽  
Riemann Tensor ◽  
Space Time ◽  
Gauge Condition ◽  
Zero Temperature ◽  
De Sitter ◽  
Abelian Gauge ◽  
Curved Space ◽  
Background Space ◽  
The One

We obtain high temperature results for the one-loop effective action for composite fields in interaction with an Abelian gauge field and minimally coupled to gravity in a curved background space-time, using the Vilkovisky-DeWitt approach, by making a local expansion in the Riemann tensor and its derivatives. We also give results for the fields minimally coupled to gravity in an arbitrary curved background space-time at zero temperature, and for the case where the fields are nonminimally coupled to gravity in Euclidean de Sitter space. The results obtained are gauge-invariant and gauge-condition-independent on-shell as well as off-shell.

The entropy evolution of a Schwarzschild–(Anti) de Sitter black hole

2020 ◽  
Vol 29 (07) ◽  
pp. 2050048
Author(s):  
Xin-Yang Wang ◽  
Yi-Ru Wang ◽  
Wen-Biao Liu
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Scalar Field ◽  
Hawking Radiation ◽  
Dynamical Variable ◽  
De Sitter ◽  
The One ◽  
Definition Of ◽  
Spherically Symmetry ◽  
Interior Volume

Based on the definition of the interior volume of spherically symmetry black holes, the interior volume of Schwarzschild–(Anti) de Sitter black holes is calculated. It is shown that with the cosmological constant ([Formula: see text]) increasing, the changing behaviors of both the position of the largest hypersurface and the interior volume for the Schwarzschild–Anti de Sitter black hole are the same as the Schwarzschild–de Sitter black hole. Considering a scalar field in the interior volume and Hawking radiation with only energy, the evolution relation between the scalar field entropy and Bekenstein–Hawking entropy is constructed. The results show that the scalar field entropy is approximately proportional to Bekenstein–Hawking entropy during Hawking radiation. Meanwhile, the proportionality coefficient is also regarded as a constant approximately with the increasing [Formula: see text]. Furthermore, considering [Formula: see text] as a dynamical variable, the modified Stefan–Boltzmann law is proposed which can be used to describe the variation of both the mass and [Formula: see text] under Hawking radiation. Using this modified law, the evolution relation between the two types of entropy is also constructed. The results show that the coefficient for Schwarzschild–de Sitter black holes is closer to a constant than the one for Schwarzschild–Anti de Sitter black holes during the evaporation process. Moreover, we find that for Hawking radiation carrying only energy, the evolution relation is a special case compared with the situation that the mass and [Formula: see text] are both considered as dynamical variables.

scholarly journals EULER–HEISENBERG LAGRANGIAN THROUGH KREIN REGULARIZATION

2013 ◽  
Vol 28 (14) ◽  
pp. 1350056 ◽  
Author(s):  
A. REFAEI
Keyword(s):  
Electromagnetic Field ◽  
Effective Action ◽  
Light Cone ◽  
Krein Space ◽  
Renormalization Procedure ◽  
Constant Electromagnetic Field ◽  
Kreĭn Space ◽  
The One ◽  
Convergent Solution ◽  
Krein Regularization

The Euler–Heisenberg effective action at the one-loop for a constant electromagnetic field is derived in Krein space quantization with Ford's idea of fluctuated light-cone. In this work, we present a perturbative but convergent solution of the effective action. Without using any renormalization procedure, the result coincides with the famous renormalized Euler–Heisenberg action.

scholarly journals SCALAR EFFECTIVE ACTION IN KREIN SPACE QUANTIZATION

2011 ◽  
Vol 26 (01) ◽  
pp. 31-41 ◽  
Author(s):  
A. REFAEI ◽  
M. V. TAKOOK
Keyword(s):  
Effective Action ◽  
Krein Space ◽  
Physical Interaction ◽  
Running Coupling ◽  
Loop Approximation ◽  
Running Coupling Constant ◽  
Kreĭn Space ◽  
Β Function ◽  
The One ◽  
Krein Space Quantization

In this paper, the λϕ4 scalar field effective action, in the one-loop approximation, is calculated by using the Krein space quantization. We show that the effective action is naturally finite and the singularity does not appear in the theory. The physical interaction mass, the running coupling constant and β-function are then calculated. The effective potential which is calculated in the Krein space quantization is different from the usual Hilbert space calculation, however we show that β-function is the same in the two different methods.

scholarly journals NEGATIVE NORM STATES IN DE SITTER SPACE AND QFT WITHOUT RENORMALIZATION PROCEDURE

2002 ◽  
Vol 11 (06) ◽  
pp. 509-518 ◽  
Author(s):  
MOHAMMAD VAHID TAKOOK
Keyword(s):  
Minkowski Space ◽  
De Sitter Space ◽  
Infrared Divergence ◽  
Space Time ◽  
Ultraviolet Divergence ◽  
De Sitter ◽  
Physical Content ◽  
Negative Norm ◽  
Minkowski Space Time ◽  
Loop Approximation

In recent papers,1,2 it has been shown that the presence of negative norm states or negative frequency solutions are indispensable for a fully covariant quantization of the minimally coupled scalar field in de Sitter space. Their presence, while leaving unchanged the physical content of the theory, offers the advantage of eliminating any ultraviolet divergence in the vacuum energy2 and infrared divergence in the two point function.3 We attempt here to extend this method to the interacting quantum field in Minkowski space-time. As an illustration of the procedure, we consider the λϕ4 theory in Minkowski space-time. The mathematical consequences of this method is the disappearance of the ultraviolet divergence to the one-loop approximation. This means, the effect of these auxiliary negative norm states is to allow an automatic renormalization of the theory in this approximation.

scholarly journals Massive Spin Zero Fields in Cosmology and the Tail-Free Property

Symmetry ◽  
2019 ◽  
Vol 11 (1) ◽  
pp. 36 ◽  
Author(s):  
Valerio Faraoni
Keyword(s):  
Scalar Field ◽  
Cosmological Constant ◽  
Wave Equations ◽  
Coupling Constant ◽  
De Sitter ◽  
Field Mass ◽  
Curved Space ◽  
Inflaton Field ◽  
Massive Spin ◽  
Huygens Principle

Fields of spin s ≥ 1 / 2 satisfying wave equations in a curved space obey the Huygens principle under certain conditions clarified by a known theorem. Here, this theorem is generalized to spin zero and applied to an inflaton field in de Sitter-like space, showing that tails of scalar radiation are an unavoidable physical feature. Requiring the absence of tails, on the contrary, necessarily implies an unnatural tuning between cosmological constant, scalar field mass, and coupling constant to the curvature.

CASIMIR EFFECT IN MULTIDIMENSIONAL QUANTUM SUPER-GRAVITIES AND SUPERSYMMETRY BREAKING

1988 ◽  
Vol 03 (14) ◽  
pp. 1391-1399 ◽  
Author(s):  
S.D. ODINTSOV
Keyword(s):  
Effective Action ◽  
Casimir Effect ◽  
Gravitational Energy ◽  
Temperature Phase ◽  
Zero Temperature ◽  
Dimensional Torus ◽  
Curved Space ◽  
Temperature Phase Transition ◽  
The One ◽  
Kaluza Klein

The one-loop effective action (the Casimir gravitational energy) of the aribitrary Einstein supergravity on the background [Formula: see text], where [Formula: see text] is the Minkowski space with non-zero temperature, Td is the d-dimensional torus, is calculated. The problem of quantum breaking of supersymmetry is discussed. The Vilkovisky-De Witt effective action in the D-dimensional Einstein gravity with the Λ-term on the background [Formula: see text] is found. An idea is expressed that a temperature phase transition in Kaluza-Klein theories is possible. For d=5 gravity, the Vilkovisky-De Witt effective action on the [Formula: see text], where [Formula: see text] is four-dimensional curved space-time with non-zero temperature, is found.

scholarly journals RELATING CALCULATIONS AND RENORMALIZATION IN AXIAL AND LORENTZ GAUGES AND GAUGE-INDEPENDENCE

2005 ◽  
Vol 20 (28) ◽  
pp. 6437-6449
Author(s):  
SATISH D. JOGLEKAR
Keyword(s):  
Wave Function ◽  
Green's Functions ◽  
Green’S Functions ◽  
Wave Function Renormalization ◽  
Renormalization Procedure ◽  
Point Function ◽  
Starting Point ◽  
Loop Approximation ◽  
The Difference ◽  
The One

We study further the recently developed formalism for the axial gauges toward the comparison of calculations and of the renormalization procedure in the axial and the Lorentz gauges. We do this in the one-loop approximation for the wave function renormalization and the identity of the β-functions in the two gauges. We take as the starting point the relation between the Green's functions in the two gauges obtained earlier. We obtain the relation between the one-loop propagators in the two gauges and locate those diagrams that contribute to the difference between the wave function renormalizations in the two gauges. We further employ this relation between the Green's functions to the case of the 3-point function and prove the identity of the β-functions in the two gauges.

scholarly journals The renormalization group and the effective action

2011 ◽  
Vol 89 (3) ◽  
pp. 277-280 ◽  
Author(s):  
D. G.C. McKeon
Keyword(s):  
Renormalization Group ◽  
Scalar Field ◽  
Gauge Field ◽  
Effective Potential ◽  
Effective Action ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
The One ◽  
External Gauge

The renormalization group is used to sum the leading-log (LL) contributions to the effective action for a large constant external gauge field in terms of the one-loop renormalization group (RG) function β, the next-to-leading-log (NLL) contributions in terms of the two-loop RG function, etc. The log-independent pieces are not determined by the RG equation, but can be fixed by considering the anomaly in the trace of the energy-momentum tensor. Similar considerations can be applied to the effective potential V for a scalar field [Formula: see text]; here the log-independent pieces are fixed by the condition [Formula: see text].

SOLITONS IN TWO-DIMENSIONAL ANTI-DE SITTER SPACE

2010 ◽  
Vol 25 (02n03) ◽  
pp. 289-299
Author(s):  
TONNIS TER VELDHUIS
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Soliton Solution ◽  
Quantum Correction ◽  
Soliton Solutions ◽  
Two Dimensional ◽  
De Sitter ◽  
Fluctuation Spectrum ◽  
Background Space ◽  
The One

Soliton solutions in a scalar field theory defined on an AdS1+1 background space-time are investigated. An analytic soliton solution is obtained in a polynomial model, and the classical soliton mass is calculated. The fluctuation spectrum around the soliton solution is determined, and the one-loop quantum correction to the soliton mass is computed in the semi-classical approximation.

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