QUANTUM FIELD THEORY ON CURVED BACKGROUNDS - A PRIMER

被引:37
|
作者
Benini, Marco [1 ,2 ,3 ]
Dappiaggi, Claudio [1 ,2 ]
Hack, Thomas-Paul [4 ]
机构
[1] Univ Pavia, Dipartimento Fis, Via Bassi 6, I-27100 Pavia, Italy
[2] Ist Nazl Fis Nucl, Sez Pavia, I-27100 Pavia, Italy
[3] Univ Hamburg, Inst Theoret Phys 2, D-22761 Hamburg, Germany
[4] Univ Genoa, Dipartimento Fis, I-16146 Genoa, Italy
来源
关键词
Quantum field theory on curved backgrounds; algebraic quantum field theory; MICROLOCAL SPECTRUM CONDITION; REEH-SCHLIEDER PROPERTY; WEAK ENERGY INEQUALITY; TIME ORDERED PRODUCTS; DIRAC FIELDS; SPACETIME MANIFOLDS; DYNAMICAL LOCALITY; HADAMARD CONDITION; PARTICLE CREATION; WICK POLYNOMIALS;
D O I
10.1142/S0217751X13300238
中图分类号
O57 [原子核物理学、高能物理学];
学科分类号
070202 ;
摘要
Goal of this paper is to introduce the algebraic approach to quantum field theory on curved backgrounds. Based on a set of axioms, first written down by Haag and Kastler, this method consists of a two-step procedure. In the first one, it is assigned to a physical system a suitable algebra of observables, which is meant to encode all algebraic relations among observables, such as commutation relations. In the second step, one must select an algebraic state in order to recover the standard Hilbert space interpretation of a quantum system. As quantum field theories possess infinitely many degrees of freedom, many unitarily inequivalent Hilbert space representations exist and the power of such approach is the ability to treat them all in a coherent manner. We will discuss in detail the algebraic approach for free fields in order to give the reader all necessary information to deal with the recent literature, which focuses on the applications to specific problems, mostly in cosmology.
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页数:49
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