Noncommutative Thermofield Dynamics

Abstract

The real-time operator formalism for thermal quantum field theories, thermofield dynamics, is formulated in terms of a path-integral approach in non-commutative spaces. As an application, the two-point function for a thermal non-commutative λφ 4 theory is derived at the one-loop level. The effect of temperature and the non-commutative parameter, competing with one another, is analyzed.

No-Cloning Theorem in Thermofield Dynamics

“…whereḠ is an unitary operator mixing |n ∈ H and |ñ ∈H by acting on the Hilbert space H ⊗H, similarlly to (16) and (17), but with a two-mode squeezing operator form 35 ,Ḡ…”

“…TFD approach has been largely applied in the study of finite temperature systems, from high energy physics 13,14,15,16,17 to quantum optics 18,19,20,21,22,23 and condensed matter physics 24,25,26 , in different contexts as gauge theories 27 , Anderson model 26 , renormalization group 28 , Casimir effect 29,30 , string field theory 31 , supersimmetry 32 , noncommutative theories 15,16 , non-classical states 21 , thermal and quantum fluctuations 33 , master equations 11 , among others 10 .…”

Realization of the noncommutative Seiberg–Witten gauge theory by fields in phase space

“…The algebraic structure of non-commutative geometries has been developed along different lines, in particular in association with c*-algebras [7]. The interest in noncommutative theories, since the 1990s, is due to a variety of applications [1,8], including abelian and non-abelian gauge theories [8][9][10][11], gravity [12,13], standard model for particles [15,16], supersymmetry [17] and in quantum Hall effect [18]. Issues such as the ultraviolet/infrared mixing and the renormalizability of noncommutative theories have been also addressed [19][20][21].…”

Renormalization of noncommutative quantum field theories

“…Gauge field theories with nonabelian gauge groups are constructed in [16,17]. Construction of thermal field theories is done in [18][19][20] while [21] discusses the twisted bosonization in two dimensional noncommutative spacetime. A comprehensive review of twisted field theories can be found in [3].…”