# Recursive parametrization and invariant phases of unitary matrices

## Abstract

We present further properties of a previously proposed recursive scheme for parametrization of n-by-n unitary matrices. We show that the factors in the recursive formula may be introduced in any desired order. The method is used to study the invariant phases of unitary matrices. The case of four-by-four unitary matrices is investigated in detail. We also address the question of how to construct symmetric unitary matrices (i.e., unitary matrices U that satisfy the condition U{sub ij}=U{sub ji}) using the recursive approach.

- Authors:

- Division of Mathematical Physics, LTH, Lund University, Box 118, S-22100 Lund (Sweden)

- Publication Date:

- OSTI Identifier:
- 20768716

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Mathematical Physics; Journal Volume: 47; Journal Issue: 1; Other Information: DOI: 10.1063/1.2159069; (c) 2006 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGEBRA; MATRICES; RECURSION RELATIONS; STANDARD MODEL; UNITARY SYMMETRY

### Citation Formats

```
Jarlskog, C.
```*Recursive parametrization and invariant phases of unitary matrices*. United States: N. p., 2006.
Web. doi:10.1063/1.2159069.

```
Jarlskog, C.
```*Recursive parametrization and invariant phases of unitary matrices*. United States. doi:10.1063/1.2159069.

```
Jarlskog, C. Sun .
"Recursive parametrization and invariant phases of unitary matrices". United States.
doi:10.1063/1.2159069.
```

```
@article{osti_20768716,
```

title = {Recursive parametrization and invariant phases of unitary matrices},

author = {Jarlskog, C.},

abstractNote = {We present further properties of a previously proposed recursive scheme for parametrization of n-by-n unitary matrices. We show that the factors in the recursive formula may be introduced in any desired order. The method is used to study the invariant phases of unitary matrices. The case of four-by-four unitary matrices is investigated in detail. We also address the question of how to construct symmetric unitary matrices (i.e., unitary matrices U that satisfy the condition U{sub ij}=U{sub ji}) using the recursive approach.},

doi = {10.1063/1.2159069},

journal = {Journal of Mathematical Physics},

number = 1,

volume = 47,

place = {United States},

year = {Sun Jan 15 00:00:00 EST 2006},

month = {Sun Jan 15 00:00:00 EST 2006}

}

DOI: 10.1063/1.2159069

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