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The success of the S-matrix in quantum field theory in Minkowski spacetime naturally demands the extension of the construction of the S-matrix in a general curved spacetime in a covariant manner. However, it is well-known that a global…

High Energy Physics - Theory · Physics 2021-10-29 Susobhan Mandal , Subhashish Banerjee

We generalize classical results in spectral graph theory and linear algebra more broadly, from the case where the underlying matrix is Hermitian to the case where it is non-Hermitian. New admissibility conditions are introduced to replace…

Spectral Theory · Mathematics 2019-05-21 Edinah K. Gnang , James M. Murphy

The quantum measurement axiom dictates that physical observables and in particular the Hamiltonian must be diagonalizable and have a real spectrum. For a time-independent Hamiltonian (with a discrete spectrum) these conditions ensure the…

Quantum Physics · Physics 2009-11-13 Ali Mostafazadeh

It is shown that the standard formulation of quantum mechanics in terms of Hermitian Hamiltonians is overly restrictive. A consistent physical theory of quantum mechanics can be built on a complex Hamiltonian that is not Hermitian but…

Quantum Physics · Physics 2008-12-18 Carl M. Bender , Dorje C. Brody , Hugh F. Jones

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…

Mathematical Physics · Physics 2015-06-12 Huai-Xin Cao , Zhi-Hua Guo , Zheng-Li Chen

We consider a dual $S$-matrix Bootstrap approach in $d\geq 3$ space-time dimensions which relies solely on the rigorously proven analyticity, crossing, and unitarity properties of the scattering amplitudes. As a proof of principle, we…

High Energy Physics - Theory · Physics 2022-01-05 Andrea Guerrieri , Amit Sever

We establish the analytic structure of the S-matrix in the complex-frequency plane for classical wave scattering on a Schwarzschild background in four space-time dimensions. Our argument relies on the analytic continuation of the…

High Energy Physics - Theory · Physics 2025-12-01 Miguel Correia , Tushar Gopalka , Giulia Isabella , Anna M. Wolz

A consistent physical theory of quantum mechanics can be built on a complex Hamiltonian that is not Hermitian but instead satisfies the physical condition of space-time reflection symmetry (PT symmetry). Thus, there are infinitely many new…

High Energy Physics - Theory · Physics 2009-11-10 Carl M. Bender , Dorje C. Brody , Hugh F. Jones

Using unitarity methods, we compute, for several massive two-dimensional models, the cut-constructible part of the one-loop 2->2 scattering S-matrices from the tree-level amplitudes. We apply our method to various integrable theories,…

High Energy Physics - Theory · Physics 2015-06-15 Lorenzo Bianchi , Valentina Forini , Ben Hoare

We study a two-dimensional exactly solvable non-Hermitian $PT-$non-symmetric quantum model with real spectrum, which is not amenable to separation of variables, by supersymmetrical methods. Here we focus attention on the property of…

High Energy Physics - Theory · Physics 2008-11-26 F. Cannata , M. V. Ioffe , D. N. Nishnianidze

A new supersymmetric approach to the analysis of dynamical symmetries for matrix quantum systems is presented. Contrary to standard one dimensional quantum mechanics where there is no role for an additional symmetry due to nondegeneracy,…

Quantum Physics · Physics 2008-11-26 A. A. Andrianov , F. Cannata , D. N. Nishnianidze , M. V. Ioffe

In recent reports, suggestions have been put forward to the effect that parity and time-reversal (PT) symmetry in quantum mechanics is incompatible with causality. It is shown here, in contrast, that PT-symmetric quantum mechanics is fully…

Quantum Physics · Physics 2016-04-07 Dorje C. Brody

We study the $S$-matrix interpretation of quantum theory in light of Categotical Quantum Mechanics. The $S$-matrix interpretation of quantum theory is shown to be a functorial semantics relating the algebras of quantum theory to the…

Quantum Physics · Physics 2017-09-15 Xiao-Kan Guo

Theories described by non-Hermitian Hamiltonians are known to possess strictly positive energy eigenvalues and exhibit unitary time evolution if the Hamiltonian is symmetric under discrete parity and time (PT) transformation. In this work,…

High Energy Physics - Theory · Physics 2025-08-04 Jeffrey Kuntz

In the context of the factorization method, we investigate the pseudo- Hermitian coherent states and its Hermitian counterpart coherent states under the generalized quantum condition in the framework of a position-dependent mass. By…

Mathematical Physics · Physics 2013-05-30 S. A. Yahiaoui , M. Bentaiba

Consider an $n \times n$ non-Hermitian random matrix $M_n$ whose entries are independent real random variables. Under suitable conditions on the entries, we study the fluctuations of the entries of $f(M_n)$ as $n$ tends to infinity, where…

Probability · Mathematics 2014-08-18 Sean O'Rourke

In this revised version we correct some mistakes, realizing the supersymmetry algebra on the exact S matrix, taking into account several phase factros. We study the constraint imposed by supersymmetry on the exact $S$-matrix of $\Complex…

High Energy Physics - Theory · Physics 2008-02-03 E. Abdalla , M. C. B. Abdalla

Hermitian symplectic spaces provide a natural framework for the extension theory of symmetric operators. Here we show that hermitian symplectic spaces may also be used to describe the solution to the factorisation problem for the scattering…

Mathematical Physics · Physics 2007-05-23 M. Harmer

Quantum operations that are perfectly admissible in non-relativistic quantum theory can enable signalling between spacelike separated regions when naively imported into quantum field theory (QFT). Prominent examples of such "impossible…

Quantum Physics · Physics 2026-02-02 Robin Simmons , Maria Papageorgiou , Marios Christodoulou , Časlav Brukner

We derive a multiplication law for free non-hermitian random matrices allowing for an easy reconstruction of the two-dimensional eigenvalue distribution of the product ensemble from the characteristics of the individual ensembles. We define…

Mathematical Physics · Physics 2015-03-19 Z. Burda , R. A. Janik , M. A. Nowak