# General boundary quantum field theory: Timelike hypersurfaces in the Klein-Gordon theory

## Abstract

We show that the real massive Klein-Gordon theory admits a description in terms of states on various timelike hypersurfaces and amplitudes associated with regions bounded by them. This realizes crucial elements of the general boundary framework for quantum field theory. The hypersurfaces considered are hyperplanes on the one hand and timelike hypercylinders on the other hand. The latter lead to the first explicit examples of amplitudes associated with finite regions of space, and admit no standard description in terms of 'initial' and 'final' states. We demonstrate a generalized probability interpretation in this example, going beyond the applicability of standard quantum mechanics.

- Authors:

- Instituto de Matematicas, UNAM Campus Morelia, C.P. 58190, Morelia, Michoacan (Mexico)

- Publication Date:

- OSTI Identifier:
- 20782688

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. D, Particles Fields; Journal Volume: 73; Journal Issue: 6; Other Information: DOI: 10.1103/PhysRevD.73.065017; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; AMPLITUDES; AXIOMATIC FIELD THEORY; KLEIN-GORDON EQUATION; NONLINEAR PROBLEMS; PROBABILITY; QUANTUM MECHANICS; RELATIVISTIC RANGE; SPACE

### Citation Formats

```
Oeckl, Robert.
```*General boundary quantum field theory: Timelike hypersurfaces in the Klein-Gordon theory*. United States: N. p., 2006.
Web. doi:10.1103/PHYSREVD.73.065017.

```
Oeckl, Robert.
```*General boundary quantum field theory: Timelike hypersurfaces in the Klein-Gordon theory*. United States. doi:10.1103/PHYSREVD.73.065017.

```
Oeckl, Robert. Wed .
"General boundary quantum field theory: Timelike hypersurfaces in the Klein-Gordon theory". United States.
doi:10.1103/PHYSREVD.73.065017.
```

```
@article{osti_20782688,
```

title = {General boundary quantum field theory: Timelike hypersurfaces in the Klein-Gordon theory},

author = {Oeckl, Robert},

abstractNote = {We show that the real massive Klein-Gordon theory admits a description in terms of states on various timelike hypersurfaces and amplitudes associated with regions bounded by them. This realizes crucial elements of the general boundary framework for quantum field theory. The hypersurfaces considered are hyperplanes on the one hand and timelike hypercylinders on the other hand. The latter lead to the first explicit examples of amplitudes associated with finite regions of space, and admit no standard description in terms of 'initial' and 'final' states. We demonstrate a generalized probability interpretation in this example, going beyond the applicability of standard quantum mechanics.},

doi = {10.1103/PHYSREVD.73.065017},

journal = {Physical Review. D, Particles Fields},

number = 6,

volume = 73,

place = {United States},

year = {Wed Mar 15 00:00:00 EST 2006},

month = {Wed Mar 15 00:00:00 EST 2006}

}

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