# THE THEORY OF QUANTIZED FIELDS. PART 3

## Abstract

In this paper we discuss the electromagnetic field, as perturbed by a prescribed current. All quantities of physical interest in various situations, eigenvalues, eigenfunctions, and transition probabilities, are derived from a general transformation function which is expressed in a non-Hermitian representation. The problems treated are: the determination of the energy-momentum eigenvalues and eigenfunctions for the isolated electromagnetic field, and the energy eigenvalues and eigenfunctions for the field perturbed by a time-independent current; the evaluation of transition probabilities and photon number expectation values for a time-dependent current that departs from zero only within a finite time interval, and for a time-dependent current that assumes non-vanishing time-independent values initially and finally. The results are applied in a discussion of the infra-red catastrophe and of the adiabatic theorem. It is shown how the latter can be exploited to give a uniform formulation for all problems requiring the evaluation of transition probabilities or eigenvalue displacements.

- Authors:

- Publication Date:

- Research Org.:
- Harvard Univ., Cambridge, MA (US)

- Sponsoring Org.:
- US Atomic Energy Commission (AEC) (US)

- OSTI Identifier:
- 4368814

- Report Number(s):
- NP-4565

TRN: US200506%%347

- DOE Contract Number:
- 6N-onr-24806

- Resource Type:
- Technical Report

- Resource Relation:
- Other Information: PBD: 1 May 1953

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; EVALUATION; EXPECTATION VALUE; TRANSFORMATIONS; CURRENTS; EIGENFUNCTIONS; EIGENVALUES; ELECTRODYNAMICS; ELECTROMAGNETIC FIELDS; ENERGY; MATHEMATICS; PHOTONS; QUANTUM ELECTRODYNAMICS; QUANTUM MECHANICS; FIELD THEORY

### Citation Formats

```
Schwinger, J.
```*THE THEORY OF QUANTIZED FIELDS. PART 3*. United States: N. p., 1953.
Web. doi:10.2172/4368814.

```
Schwinger, J.
```*THE THEORY OF QUANTIZED FIELDS. PART 3*. United States. doi:10.2172/4368814.

```
Schwinger, J. Fri .
"THE THEORY OF QUANTIZED FIELDS. PART 3". United States.
doi:10.2172/4368814. https://www.osti.gov/servlets/purl/4368814.
```

```
@article{osti_4368814,
```

title = {THE THEORY OF QUANTIZED FIELDS. PART 3},

author = {Schwinger, J.},

abstractNote = {In this paper we discuss the electromagnetic field, as perturbed by a prescribed current. All quantities of physical interest in various situations, eigenvalues, eigenfunctions, and transition probabilities, are derived from a general transformation function which is expressed in a non-Hermitian representation. The problems treated are: the determination of the energy-momentum eigenvalues and eigenfunctions for the isolated electromagnetic field, and the energy eigenvalues and eigenfunctions for the field perturbed by a time-independent current; the evaluation of transition probabilities and photon number expectation values for a time-dependent current that departs from zero only within a finite time interval, and for a time-dependent current that assumes non-vanishing time-independent values initially and finally. The results are applied in a discussion of the infra-red catastrophe and of the adiabatic theorem. It is shown how the latter can be exploited to give a uniform formulation for all problems requiring the evaluation of transition probabilities or eigenvalue displacements.},

doi = {10.2172/4368814},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Fri May 01 00:00:00 EDT 1953},

month = {Fri May 01 00:00:00 EDT 1953}

}