Related papers: Instantons, analytic continuation, and $\mathcal{P…
Recently, Ai, Bender and Sarkar gave a prescription on how to obtain $\mathcal{PT}$-symmetric field theory results from an analytic continuation of Hermitian field theories. I perform this analytic continuation for the massless (critical)…
We consider the $\mathcal{PT}$-symmetric quantum field theory on the noncommutative spacetime with angular twist and construct its pseudo-Hermitian interpretation. We explore the differences between internal and spatial parities in the…
Relativistic PT-symmetric fermionic interacting systems are studied in 1+1 and 3+1 dimensions. The objective is to include non-Hermitian PT-symmetric interaction terms that give {\it real} spectra. Such interacting systems could describe…
A quantum-mechanical theory is PT-symmetric if it is described by a Hamiltonian that commutes with PT, where the operator P performs space reflection and the operator T performs time reversal. A PT-symmetric Hamiltonian often has a…
Some quantum field theories described by non-Hermitian Hamiltonians are investigated. It is shown that for the case of a free fermion field theory with a $\gamma_5$ mass term the Hamiltonian is $\cal PT$-symmetric. Depending on the mass…
Interacting quantum scalar field theories in $dS_D\times M_d$ spacetime can be reduced to Euclidean field theories in $M_d$ space in the vicinity of $I_+$ infinity of $dS_D$ spacetime. Using this non-perturbative mapping, we analyze the…
The spectrum of the Hermitian Hamiltonian ${1\over2}p^2+{1\over2}m^2x^2+gx^4$ ($g>0$), which describes the quantum anharmonic oscillator, is real and positive. The non-Hermitian quantum-mechanical Hamiltonian $H={1\over2}p^2+{1…
The scalar field theory with potential $V(\varphi)=\textstyle{\frac{1}{2}} m^2\varphi^2-\textstyle{\frac{1}{4}} g\varphi^4$ ($g>0$) is ill defined as a Hermitian theory but in a non-Hermitian $\mathcal{P}\mathcal{T}$-symmetric framework it…
We develop relativistic non-Hermitian quantum theory and its application to neutrino physics in a strong magnetic field. It is well known, that one of the fundamental postulates of quantum theory is the requirement of Hermiticity of…
Perturbative PT-symmetric quantum field theories with anti-Hermitian and P-odd interaction terms are studied in path integral formalism and the i phi^3 model is calculated in detail. The nonlocal field transformation induced by the C…
We construct PT-symmetric quantum mechanical models with an O(N)-symmetric interaction term of the form $-g(\vec{x}^{2})^{2}/N$. Using functional integral methods, we find the equivalent Hermitian model, which has several unusual features.…
We introduce hermiticity as a new symmetry and show that when starting with a model which is Hermitian in the classical level, quantum corrections can break hermiticity while the theory stay physically acceptable. To show this, we…
PT-symmetric quantum theory was originally proposed with the aim of extending standard quantum theory by relaxing the Hermiticity constraint on Hamiltonians. However, no such extension has been formulated that consistently describes states,…
It is generally assumed that a Hamiltonian for a physically acceptable quantum system (one that has a positive-definite spectrum and obeys the requirement of unitarity) must be Hermitian. However, a PT-symmetric Hamiltonian can also define…
A comparative analysis of a model of complex scalar field $\phi$ and real scalar field $\chi$ with interaction $g\phi^*\phi\chi$ for the real and purely imaginary values of coupling $g$ in perturbative and non-perturbative regions. In…
We review how to describe a field theory that includes a non-Hermitian mass term in the region of parameter space where the Lagrangian is $PT$-symmetric. The discrete symmetries of the system are essential for understanding the consistency…
To lowest order of perturbation theory we show that an equivalence can be established between a $\cal PT$-symmetric generalized quartic anharmonic oscillator model and a Hermitian position-dependent mass Hamiltonian $h$. An important…
Recently, it was observed that self-interacting scalar quantum field theories having a non-Hermitian interaction term of the form $g(i\phi)^{2+\delta}$, where $\delta$ is a real positive parameter, are physically acceptable in the sense…
The coupling of non-Hermitian PT-symmetric Hamiltonians to standard Hermitian Hamiltonians, each of which individually has a real energy spectrum, is explored by means of a number of soluble models. It is found that in all cases the energy…
PT-symmetric quantum mechanics is an alternative formulation of quantum mechanics in which the mathematical axiom of Hermiticity (transpose and complex conjugate) is replaced by the physically transparent condition of space-time reflection…