A remark on formal KMS states in deformation quantization

被引：22

作者：

Bordemann, M ^{[1
]}

Romer, H ^{[1
]}

Waldmann, S ^{[1
]}

机构：

[1] Univ Freiburg, Fak Phys, D-79104 Freiburg, Germany

来源：

LETTERS IN MATHEMATICAL PHYSICS | 1998年 / 45卷 / 01期

关键词：

deformation quantization; KMS states;

D O I：

10.1023/A:1007481019610

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

Within the framework of deformation quantization, we define formal KMS states on the deformed algebra of power series of functions with compact support in phase space as C[[lambda]]-linear functionals obeying a formal variant of the usual KMS condition known in the theory of C*-algebras. We show that for each temperature KMS states always exist and are up to a normalization equal to the trace of the argument multiplied by a formal analogue of the usual Boltzmann factor, a certain formal star exponential.

引用

页码：49 / 61

页数：13

共 28 条

[11]

BORDEMANN M, 1996, QALG9607019

[12]

BORDEMANN M, 1997, QALG9711016

[13]

Bratteli O., 1981, OPERATOR ALGEBRAS QU, VI

[14]

Bratteli O., 1981, TEXTS MONOGRAPHS PHY

[15] CLOSED STAR PRODUCTS AND CYCLIC COHOMOLOGY [J].

CONNES, A ;

FLATO, M ;

STERNHEIMER, D .

LETTERS IN MATHEMATICAL PHYSICS, 1992, 24 (01) :1-12

[16]

Connes A., 1994, NONCOMMUTATIVE GEOME

[17] EXISTENCE OF STAR-PRODUCTS AND OF FORMAL DEFORMATIONS OF THE POISSON LIE-ALGEBRA OF ARBITRARY SYMPLECTIC-MANIFOLDS [J].

DEWILDE, M ;

LECOMTE, PBA .

LETTERS IN MATHEMATICAL PHYSICS, 1983, 7 (06) :487-496

[18]

DEWILDE M, 1988, DEFORMATION THEORY A

[19]

Fedosov Boris, 1996, MATH TOPICS, V9

[20] CLASSICAL KMS BOUNDARY-CONDITION [J].

GALLAVOTTI, G ;

VERBOVEN, E .

NUOVO CIMENTO DELLA SOCIETA ITALIANA DI FISICA B-GENERAL PHYSICS RELATIVITY ASTRONOMY AND MATHEMATICAL PHYSICS AND METHODS, 1975, 28 (01) :274-286

← 1 2 3 →