# PT-Symmetric Quantum Field Theory

## Abstract

In 1998 it was discovered that the requirement that a Hamiltonian be Dirac Hermitian (H = H{sup {dagger}}) can be weakened and generalized to the requirement that a Hamiltonian be PT symmetric ([H,PT] = 0); that is, invariant under combined space reflection and time reversal. Weakening the constraint of Hermiticity allows one to consider new kinds of physically acceptable Hamiltonians and, in effect, it amounts to extending quantum mechanics from the real (Hermitian) domain into the complex domain. Much work has been done on the analysis of various PT-symmetric quantum-mechanical models. However, only very little analysis has been done on PT-symmetric quantum-field-theoretic models. Here, we describe some of what has been done in the context of PT-symmetric quantum field theory and describe some possible fundamental applications.

- Authors:

- Physics Department, Washington University, St. Louis, MO 63130 (United States)

- Publication Date:

- OSTI Identifier:
- 21611608

- Resource Type:
- Journal Article

- Journal Name:
- AIP Conference Proceedings

- Additional Journal Information:
- Journal Volume: 1389; Journal Issue: 1; Conference: ICNAAM 2011: Conference on numerical analysis and applied mathematics, Halkidiki (Greece), 19-25 Sep 2011; Other Information: DOI: 10.1063/1.3636813; (c) 2011 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0094-243X

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; AXIOMATIC FIELD THEORY; DIRAC EQUATION; HAMILTONIANS; LAGRANGIAN FIELD THEORY; P INVARIANCE; QUANTUM MECHANICS; SYMMETRY; SYMMETRY BREAKING; T INVARIANCE; DIFFERENTIAL EQUATIONS; EQUATIONS; FIELD EQUATIONS; FIELD THEORIES; INVARIANCE PRINCIPLES; MATHEMATICAL OPERATORS; MECHANICS; PARTIAL DIFFERENTIAL EQUATIONS; QUANTUM FIELD THEORY; QUANTUM OPERATORS; WAVE EQUATIONS

### Citation Formats

```
Bender, Carl M.
```*PT-Symmetric Quantum Field Theory*. United States: N. p., 2011.
Web. doi:10.1063/1.3636813.

```
Bender, Carl M.
```*PT-Symmetric Quantum Field Theory*. United States. doi:10.1063/1.3636813.

```
Bender, Carl M. Thu .
"PT-Symmetric Quantum Field Theory". United States. doi:10.1063/1.3636813.
```

```
@article{osti_21611608,
```

title = {PT-Symmetric Quantum Field Theory},

author = {Bender, Carl M.},

abstractNote = {In 1998 it was discovered that the requirement that a Hamiltonian be Dirac Hermitian (H = H{sup {dagger}}) can be weakened and generalized to the requirement that a Hamiltonian be PT symmetric ([H,PT] = 0); that is, invariant under combined space reflection and time reversal. Weakening the constraint of Hermiticity allows one to consider new kinds of physically acceptable Hamiltonians and, in effect, it amounts to extending quantum mechanics from the real (Hermitian) domain into the complex domain. Much work has been done on the analysis of various PT-symmetric quantum-mechanical models. However, only very little analysis has been done on PT-symmetric quantum-field-theoretic models. Here, we describe some of what has been done in the context of PT-symmetric quantum field theory and describe some possible fundamental applications.},

doi = {10.1063/1.3636813},

journal = {AIP Conference Proceedings},

issn = {0094-243X},

number = 1,

volume = 1389,

place = {United States},

year = {2011},

month = {9}

}