Symplectic Field Theories: Scalar and Spinor Representations

被引：2

作者：

Costa, Caroline ^{[1
,2
]}

Tenser, Marcia R. ^{[1
]}

Amorim, Ronni G. G. ^{[1
,3
]}

Fernandes, Marco C. B. ^{[1
]}

Santana, Ademir E. ^{[1
]}

Vianna, J. David M. ^{[1
,4
]}

机构：

[1] Univ Brasilia, Inst Fis, Int Ctr Phys, BR-70910900 Brasilia, DF, Brazil

[2] Univ Estadual Paulista, Inst Fis Teor, BR-01140070 Sao Paulo, SP, Brazil

[3] Univ Brasilia, Fac Gama, BR-72444240 Brasilia, DF, Brazil

[4] Univ Fed Bahia, Inst Fis, BR-40210340 Salvador, BA, Brazil

来源：

ADVANCES IN APPLIED CLIFFORD ALGEBRAS | 2018年 / 28卷 / 01期

关键词：

Moyal product; Phase space; Field theory; PHASE-SPACE; QUANTUM-MECHANICS; WIGNER FUNCTIONS; DENSITY-MATRIX; NONCOMMUTATIVE GEOMETRY; PHOTON DISTRIBUTION; QUANTIZATION; ALGEBRA; STATES; LIGHT;

D O I：

10.1007/s00006-018-0840-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Using elements of symmetry, as gauge invariance, aspects of field theories represented in symplectic space are introduced and analyzed under physical bases. The states of a system are described by symplectic wave functions, which are associated with the Wigner function. Such wave functions are vectors in a Hilbert space introduced from the cotangent-bundle of the Minkowski space. The symplectic Klein-Gordon and the Dirac equations are derived, and a minimum coupling is considered in order to analyze the Landau problem in phase space.

引用

页数：18

共 53 条

[1] The Cangemi-Jackiw manifold in high dimensions and symplectic structure [J].

Abreu, LM ;

Santana, AE ;

Ribeiro, A .

ANNALS OF PHYSICS, 2002, 297 (02) :396-408

[2] Wigner functions for curved spaces. I. On hyperboloids [J].

Alonso, MA ;

Pogosyan, GS ;

Wolf, KB .

JOURNAL OF MATHEMATICAL PHYSICS, 2002, 43 (12) :5857-5871

[3] Non-commutative geometry and symplectic field theory [J].

Amorim, R. G. G. ;

Fernandes, M. C. B. ;

Khanna, F. C. ;

Santana, A. E. ;

Vianna, J. D. M. .

PHYSICS LETTERS A, 2007, 361 (06) :464-471

[4] Realization of the noncommutative Seiberg-Witten gauge theory by fields in phase space [J].

Amorim, R. G. G. ;

Khanna, F. C. ;

Malbouisson, A. P. C. ;

Malbouisson, J. M. C. ;

Santana, A. E. .

INTERNATIONAL JOURNAL OF MODERN PHYSICS A, 2015, 30 (22)

[5] The Noncommutative Harmonic Oscillator Based on Symplectic Representation of Galilei Group [J].

Amorim, R. G. G. ;

Ulhoa, S. C. ;

Santana, A. E. .

BRAZILIAN JOURNAL OF PHYSICS, 2013, 43 (1-2) :78-85

[6] Perturbative symplectic field theory and Wigner function [J].

Amorim, Ronni G. G. ;

Khanna, Faqir C. ;

Santana, Ademir E. ;

Vianna, Jose David M. .

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2009, 388 (18) :3771-3778

[7] Poincare-Lie algebra and relativistic phase space [J].

Andrade, MCB ;

Santana, AE ;

Vianna, JDM .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2000, 33 (22) :4015-4024

[8]

[Anonymous], 1999, Journal of High Energy Physics

[9] THE NONCOMMUTATIVE GEOMETRY OF THE QUANTUM HALL-EFFECT [J].

BELLISSARD, J ;

VANELST, A ;

SCHULZBALDES, H .

JOURNAL OF MATHEMATICAL PHYSICS, 1994, 35 (10) :5373-5451

[10] EXPONENTIAL APPROXIMATION FOR THE DENSITY-MATRIX AND THE WIGNER DISTRIBUTION [J].

BERKOWITZ, M .

CHEMICAL PHYSICS LETTERS, 1986, 129 (05) :486-488

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