Uniformly accelerated observer in Moyal spacetime Authors Nirmalendu Acharyya Centre for High Energy Physics Indian Institute of Science Sachindeo Vaidya Centre for High Energy Physics Indian Institute of Science Article

First Online: 14 September 2010 Received: 09 June 2010 Revised: 28 July 2010 Accepted: 16 August 2010 DOI :
10.1007/JHEP09(2010)045

Cite this article as: Acharyya, N. & Vaidya, S. J. High Energ. Phys. (2010) 2010: 45. doi:10.1007/JHEP09(2010)045
Abstract In Minkowski space, an accelerated reference frame may be defined as one that is related to an inertial frame by a sequence of instantaneous Lorentz transformations. Such an accelerated observer sees a causal horizon, and the quantum vacuum of the inertial observer appears thermal to the accelerated observer, also known as the Unruh effect. We argue that an accelerating frame may be similarly defined (i.e. as a sequence of instantaneous Lorentz transformations) in noncommutative Moyal spacetime, and discuss the twisted quantum field theory appropriate for such an accelerated observer. Our analysis shows that there are several new features in the case of noncommutative space-time: chiral massless fields in (1 + 1) dimensions have a qualitatively different behavior compared to massive fields. In addition, the vacuum of the inertial observer is no longer an equilibrium thermal state of the accelerating observer, and the Bose-Einstein distribution acquires θ -dependent corrections.

Keywords Non-Commutative Geometry Thermal Field Theory Space-Time Symmetries

References [1]

S. Doplicher, K. Fredenhagen and J.E. Roberts,

The Quantum structure of space-time at the Planck scale and quantum fields ,

Commun. Math. Phys.
172 (1995) 187 [

hep-th/0303037 ] [

SPIRES ].

MathSciNet ADS MATH CrossRef [2]

D. Bahns, S. Doplicher, K. Fredenhagen and G. Piacitelli,

Quantum Geometry on Quantum Spacetime: Distance, Area and Volume Operators ,

arXiv:1005.2130 [

SPIRES ].

[3]

R.J. Hughes,

Uniform acceleration and the quantum field theory vacuum, I ,

Annals Phys.
162 (1985) 1 [

SPIRES ].

ADS CrossRef [4]

L.C.B. Crispino, A. Higuchi and G.E.A. Matsas,

The Unruh effect and its applications ,

Rev. Mod. Phys.
80 (2008) 787 [

arXiv:0710.5373 ] [

SPIRES ].

MathSciNet ADS MATH CrossRef [5]

P. Aschieri et al.,

A gravity theory on noncommutative spaces ,

Class. Quant. Grav.
22 (2005) 3511 [

hep-th/0504183 ] [

SPIRES ].

MathSciNet ADS MATH CrossRef [6]

M. Chaichian, P.P. Kulish, K. Nishijima, A. Tureanu,

On a Lorentz-invariant interpretation of noncommutative space-time and its implications on noncommutative QFT ,

Phys. Lett.
B 604 (2004) 98 [

hep-th/0408069 ] [

SPIRES ].

MathSciNet ADS [7]

J. Wess,

Deformed coordinate spaces: Derivatives , lectures given at

BW 2003 Workshop on Mathematical, Theoretical and Phenomenological Challenges Beyond the Standard Model: Perspectives of Balkans Collaboration , Vrnjacka Banja, Serbia, August 29–September 2 2003

hep-th/0408080 [

SPIRES ].

[8]

A.P. Balachandran, G. Mangano, A. Pinzul and S. Vaidya,

Spin and statistics on the Groenwald-Moyal plane: Pauli-forbidden levels and transitions ,

Int. J. Mod. Phys.
A 21 (2006) 3111 [

hep-th/0508002 ] [

SPIRES ].

MathSciNet ADS [9]

A.P. Balachandran, T.R. Govindarajan, G. Mangano, A. Pinzul, B.A. Qureshi and S. Vaidya,

Statistics and UV-IR mixing with twisted Poincar´e invariance ,

Phys. Rev.
D 75 (2007) 045009 [

hep-th/0608179 ] [

SPIRES ].

ADS [10]

A.P. Balachandran, A. Pinzul and B.A. Qureshi,

UV-IR Mixing in Non-Commutative Plane ,

Phys. Lett.
B 634 (2006) 434 [

hep-th/0508151 ] [

SPIRES ].

MathSciNet ADS [11]

S. Majid,

Foundations of Quantum Group Theory , Cambridge University Press, Cambridge U.K. (1995).

MATH CrossRef [12]

H. Grosse,

On the construction of Möller operators for the nonlinear schrodinger equation ,

Phys. Lett.
B 86 (1979) 267.

MathSciNet ADS [13]

A.B. Zamolodchikov and Al.B. Zamolodchikov,

Factorized S-matrices in two dimensions as the exact solutions of certain relativistic quantum field theory models ,

Annals Phys.
120 (1979) 253.

MathSciNet ADS CrossRef [14]

L.D. Faddeev,

Quantum completely integral models of field theory ,

Sov. Sci. Rev. C
1 (1980) 107 [

SPIRES ].

[15]

S. Takagi,

Vacuum Noise And Stress Induced By Uniform Accelerator: Hawking-Unruh Effect In Rindler Manifold Of Arbitrary Dimensions ,

Prog. Theor. Phys. Suppl.
88 (1986) 1 [

SPIRES ].

MathSciNet ADS CrossRef [16]

H. Grosse and G. Lechner,

Wedge-Local Quantum Fields and Noncommutative Minkowski Space ,

JHEP
11 (2007) 012 [

arXiv:0706.3992 ] [

SPIRES ].

MathSciNet ADS CrossRef [17]

S. Wienberg, The Quantum Theory of Fields, Volume I , Cambridge University Press, Cambridge U.K. (1995).

[18]

J.J. Bisognano and E.H. Wichmann,

On The Duality Condition For Quantum Fields ,

J. Math. Phys.
17 (1976) 303 [

SPIRES ].

MathSciNet ADS CrossRef [19]

J.J. Bisognano and E.H. Wichmann,

On The Duality Condition For A Hermitian Scalar Field ,

J. Math. Phys.
16 (1975) 985 [

SPIRES ].

MathSciNet ADS MATH CrossRef [20]

G.L. Sewell,

Quantum fields on manifolds: PCT and gravitationally induced thermal states ,

Annals Phys.
141 (1982) 201 [

SPIRES ].

MathSciNet ADS CrossRef [21]

S.A. Fulling and S.N.M. Ruijsenaars,

Temperature, periodicity, and horizons ,

Phys. Rept.
152 (1987) 135.

MathSciNet ADS CrossRef [22]

U.H. Gerlach,

Minkowski Bessel modes ,

Phys. Rev.
D 38 (1988) 514 [

gr-qc/9910097 ] [

SPIRES ].

MathSciNet ADS © SISSA, Trieste, Italy 2010