Scattering in Algebraic Approach to Quantum Theory-Associative Algebras

被引:3
作者
Schwarz, Albert [1 ]
机构
[1] Univ Calif Davis, Dept Math, Davis, CA 95616 USA
关键词
inclusive scattering matrix; generalized Green functions; associative algebras; FORMALISM;
D O I
10.3390/universe8120660
中图分类号
P1 [天文学];
学科分类号
0704 ;
摘要
The definitions of scattering matrix and inclusive scattering matrix in the framework of formulation of quantum field theory in terms of associative algebras with involution are presented. The scattering matrix is expressed in terms of Green functions on shell (LSZ formula), and the inclusive scattering matrix is expressed in terms of generalized Green functions on shell. The expression for inclusive scattering matrix can be used also for quasi-particles (for elementary excitations of any translation-invariant stationary state, for example, for elementary excitations of equilibrium state). An interesting novelty is the consideration of associative algebras over real numbers.
引用
收藏
页数:15
相关论文
共 15 条
[1]  
Araki H., 1967, COMMUN MATH PHYS, V4, P77, DOI [10.1007/BF01645754, DOI 10.1007/BF01645754]
[2]   EQUILIBRIUM AND NONEQUILIBRIUM FORMALISMS MADE UNIFIED [J].
CHOU, KC ;
SU, ZB ;
HAO, BL ;
YU, L .
PHYSICS REPORTS-REVIEW SECTION OF PHYSICS LETTERS, 1985, 118 (1-2) :1-131
[3]   A UNIFIED FORMALISM OF THERMAL QUANTUM-FIELD THEORY [J].
CHU, H ;
UMEZAWA, H .
INTERNATIONAL JOURNAL OF MODERN PHYSICS A, 1994, 9 (14) :2363-2409
[4]  
Fateev V.A., 1973, TEOR MAT FIZ, V14, P152, DOI [DOI 10.1007/BF01036349, 10.1007/BF01036349]
[5]   The quantum N-body problem [J].
Hunziker, W ;
Sigal, IM .
JOURNAL OF MATHEMATICAL PHYSICS, 2000, 41 (06) :3448-3510
[6]   Keldysh technique and non-linear σ-model: basic principles and applications [J].
Kamenev, Alex ;
Levchenko, Alex .
ADVANCES IN PHYSICS, 2009, 58 (03) :197-319
[7]  
Kapustin A., 2013, ARXIV
[8]   Geometric and algebraic approaches to quantum theory [J].
Schwarz, A. .
NUCLEAR PHYSICS B, 2021, 973
[9]   Inclusive scattering matrix and scattering of quasiparticles [J].
Schwarz, A. .
NUCLEAR PHYSICS B, 2020, 950
[10]  
Schwarz A, 2020, MATH FDN QUANTUM FIE