scholarly journals Erratum: Extension ofPT-symmetric quantum mechanics to quantum field theory with cubic interaction [Phys. Rev. D70, 025001 (2004)]

2005 ◽  
Vol 71 (4) ◽  
Author(s):  
Carl M. Bender ◽  
Dorje C. Brody ◽  
Hugh F. Jones
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Mechanics ◽  
Quantum Field ◽  
Symmetric Quantum

NON-HERMITIAN QUANTUM FIELD THEORY

2005 ◽  
Vol 20 (19) ◽  
pp. 4646-4652 ◽  
Author(s):  
CARL. M. BENDER
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Mechanics ◽  
Degrees Of Freedom ◽  
Real Spectrum ◽  
Quantum Field ◽  
Unitary Theory ◽  
Symmetric Quantum ◽  
Quantum Mechanical Systems ◽  
Bounded Below

In my talk at the Seventh QCD Workshop held in Villefranche in January 2003 I showed that a non-Hermitian Hamiltonian H possessing an unbroken [Formula: see text] symmetry (i) has a real spectrum that is bounded below, and (ii) defines a unitary theory of quantum mechanics with positive norm. The proof of unitarity requires a linear operator [Formula: see text], which was originally defined as a sum over the eigenfunctions of H. However, using this definition to calculate [Formula: see text] is cumbersome in quantum mechanics and impossible in quantum field theory. I describe here an alternative method for calculating [Formula: see text] directly in terms of the operator dynamical variables of the quantum theory. This new method is general and applies to a variety of quantum mechanical systems having several degrees of freedom. More importantly, this method gives the [Formula: see text] operator in quantum field theory. The [Formula: see text] operator is a new time-independent observable in [Formula: see text]-symmetric quantum field theory.

Quantum mechanics

2018 ◽  
Author(s):  
Michael Kachelriess
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Mechanics ◽  
Relativistic Quantum ◽  
Transition Amplitude ◽  
External Source ◽  
Quantum Field ◽  
Damping Term ◽  
Relativistic Quantum Theory ◽  
Generating Functional

After a brief review of the operator approach to quantum mechanics, Feynmans path integral, which expresses a transition amplitude as a sum over all paths, is derived. Adding a linear coupling to an external source J and a damping term to the Lagrangian, the ground-state persistence amplitude is obtained. This quantity serves as the generating functional Z[J] for n-point Green functions which are the main target when studying quantum field theory. Then the harmonic oscillator as an example for a one-dimensional quantum field theory is discussed and the reason why a relativistic quantum theory should be based on quantum fields is explained.

QLB for Quantum Many-Body and Quantum Field Theory

2018 ◽  
Author(s):  
Sauro Succi
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Mechanics ◽  
Quantum Computing ◽  
Single Particle ◽  
Body Problem ◽  
Three Dimensions ◽  
Quantum Field ◽  
Many Body ◽  
Quantum Particles

Chapter 32 expounded the basic theory of quantum LB for the case of relativistic and non-relativistic wavefunctions, namely single-particle quantum mechanics. This chapter goes on to cover extensions of the quantum LB formalism to the overly challenging arena of quantum many-body problems and quantum field theory, along with an appraisal of prospective quantum computing implementations. Solving the single particle Schrodinger, or Dirac, equation in three dimensions is a computationally demanding task. This task, however, pales in front of the ordeal of solving the Schrodinger equation for the quantum many-body problem, namely a collection of many quantum particles, typically nuclei and electrons in a given atom or molecule.

Hyper-asymptotic expansions and instantons

2019 ◽  
pp. 471-492
Author(s):  
Jean Zinn-Justin
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Mechanics ◽  
Asymptotic Expansions ◽  
Perturbative Expansion ◽  
Quantum Field ◽  
Wkb Method ◽  
Additional Information ◽  
Spectral Equation ◽  
Double Well Potential

Chapter 24 examines the topic of hyper–asymptotic expansions and instantons. A number of quantum mechanics and quantum field theory (QFT) examples exhibit degenerate classical minima connected by quantum barrier penetration effects. The analysis of the large order behaviour, based on instanton calculus, shows that the perturbative expansion is not Borel summable, and does not define unique functions. An important issue is then what kind of additional information is required to determine the exact expanded functions. While the QFT examples are complicated, and their study is still at the preliminary stage, in quantum mechanics, in the case of some analytic potentials that have degenerate minima (like the quartic double–well potential), the problem has been completely solved. Some examples are described in Chapter 24. There, the perturbative, complete, hyper–asymptotic expansion exhibits the resurgence property. The perturbative expansion can be related to the calculation of the spectral equation via the complex WKB method.

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