scholarly journals New ansatz for metric operator calculation in pseudo-Hermitian field theory

2009 ◽  
Vol 79 (10) ◽  
Author(s):  
Abouzeid M. Shalaby
Keyword(s):  
Field Theory ◽  
Metric Operator ◽  
Operator Calculation

scholarly journals Comment on “New ansatz for metric operator calculation in pseudo-Hermitian field theory”

2009 ◽  
Vol 80 (12) ◽  
Author(s):  
Carl M. Bender ◽  
Gregorio Benincasa ◽  
H. F. Jones
Keyword(s):  
Field Theory ◽  
Metric Operator ◽  
Operator Calculation

scholarly journals VACUUM STABILITY OF THE ${\mathcal{PT}}$-SYMMETRIC (-ϕ4) SCALAR FIELD THEORY

2013 ◽  
Vol 28 (08) ◽  
pp. 1350023 ◽  
Author(s):  
ABOUZEID M. SHALABY
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Effective Potential ◽  
Canonical Quantization ◽  
Field Potential ◽  
Space Time ◽  
Effective Field ◽  
Vacuum Stability ◽  
Metric Operator ◽  
Equal Time Commutation

In this paper, we study the vacuum stability of the classical unstable (-ϕ4) scalar field potential. Regarding this, we obtained the effective potential, up to second-order in the coupling, for the theory in 1+1 and 2+1 space–time dimensions. We found that the obtained effective potential is bounded-from-below, which proves the vacuum stability of the theory in space–time dimensions higher than the previously studied 0+1 case. In our calculations, we used the canonical quantization regime in which one deals with operators rather than classical functions used in the path integral formulation. Therefore, the non-Hermiticity of the effective field theory is obvious. Moreover, the method we employ implements the canonical equal-time commutation relations and the Heisenberg picture for the operators. Thus, the metric operator is implemented in the calculations of the transition amplitudes. Accordingly, the method avoids the very complicated calculations needed in other methods for the metric operator. To test the accuracy of our results, we obtained the exponential behavior of the vacuum condensate for small coupling values, which has been obtained in the literature using other methods. We assert that this work is interesting, as all the studies in the literature advocate the stability of the (-ϕ4) theory at the quantum mechanical level while our work extends the argument to the level of field quantization.

scholarly journals REPRESENTATION DEPENDENCE OF SUPERFICIAL DEGREE OF DIVERGENCES IN QUANTUM FIELD THEORY

2011 ◽  
Vol 26 (17) ◽  
pp. 2913-2925 ◽  
Author(s):  
ABOUZEID M. SHALABY
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Vacuum Energy ◽  
Space Time ◽  
Feynman Diagrams ◽  
Coupling Constants ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Metric Operator

In this work, we investigate a very important but unstressed result in the work of C. M. Bender, J.-H. Chen, and K. A. Milton, J. Phys. A39, 1657 (2006). These authors have calculated the vacuum energy of the iϕ3 scalar field theory and its Hermitian equivalent theory up to g4 order of calculations. While all the Feynman diagrams of the iϕ3 theory are finite in 0+1 space–time dimensions, some of the corresponding Feynman diagrams in the equivalent Hermitian theory are divergent. In this work, we show that the divergences in the Hermitian theory originate from superrenormalizable, renormalizable and nonrenormalizable terms in the interaction Hamiltonian even though the calculations are carried out in the 0+1 space–time dimensions. Relying on this interesting result, we raise a question: Is the superficial degree of divergence of a theory is representation dependent? To answer this question, we introduce and study a class of non-Hermitian quantum field theories characterized by a field derivative interaction Hamiltonian. We showed that the class is physically acceptable by finding the corresponding class of metric operators in a closed form. We realized that the obtained equivalent Hermitian and the introduced non-Hermitian representations have coupling constants of different mass dimensions which may be considered as a clue for the possibility of considering nonrenormalizability of a field theory as a nongenuine problem. Besides, the metric operator is supposed to disappear from path integral calculations which means that physical amplitudes can be fully obtained in the simpler non-Hermitian representation.

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