Quantisation of Lorentz invariant scalar field theory in non-commutative space-time and its consequence

Abstract

Quantisation of Lorentz invariant scalar field theory in Doplicher-Fredenhagen-Roberts (DFR) space-time, a Lorentz invariant, non-commutative space-time is studied. Absence of a unique Lagrangian in non-commutative space-time necessitates us to use an approach to quantisation that is based on the equations of motion alone. Using this we derive the equal time commutation relation between Doplicher-Fredenhagen-Roberts-Amorim (DFRA) scalar field and its conjugate, which has non-commutative dependent modifications, but the corresponding creation and annihilation operators obey usual algebra. We show that imposing the condition that the commutation relation between the field and its conjugate is same as that in the commutative space-time leads to a deformation of the algebra of quantised oscillators. Both these deformed commutation relations derived are valid to all orders in the non-commutative parameter. By analysing the first non-vanishing terms which are ${\theta }^3$ order, we show that the deformed commutaton relations scale as $1/{\lambda }^4$, where $\lambda$ is the length scale set by the non-commutativity of the space-time. We also derive the conserved currents for DFRA scalar field. Further, we analyse the effects of non-commutativity on Unruh effect by analysing a detector coupled to the DFRA scalar field, showing that the Unruh temperature is not modified but the thermal radiation seen by the accelerated observer gets correction due to the non-commutativity of space-time.

arXiv comment25 pages

References in corpus (29)

• Noncommutative Field Theory
• Quantum Field Theory on Noncommutative Spaces
• The quantum structure of spacetime at the Planck scale and quantum fields
• The Unruh effect and its applications
• On a Lorentz-Invariant Interpretation of Noncommutative Space-Time and Its Implications on Noncommutative QFT
• Space-Time Noncommutative Field Theories And Unitarity
• A Gravity Theory on Noncommutative Spaces
• Deformed Field Theory on kappa-spacetime
• New realizations of Lie algebra kappa-deformed Euclidean space
• Noncommutative Quantum Gravity
• Quantum Theories on Noncommutative Spaces with Nontrivial Topology: Aharonov-Bohm and Casimir Effects
• Noncommutative Field Theories and Gravity
• Noncommutative Gravity
• Deformed Oscillator Algebras and QFT in $\kappa$-Minkowski Spacetime
• Exact Seiberg-Witten Map, Induced Gravity and Topological Invariants in Noncommutative Field Theories
• Noncommutative Gauge Theory without Lorentz Violation
• More on Mixed Boundary Conditions and D-branes Bound States
• Generalized Poincare algebras, Hopf algebras and kappa-Minkowski spacetime
• Lorentz-Invariant Non-Commutative Space-Time Based On DFR Algebra
• Comments on the Energy-Momentum Tensor in Non-Commutative Field Theories
• Lorentz Invariance And Unitarity Problem In Non-Commutative Field Theory
• Unusual High-Energy Phenomenology of Lorentz-Invariant Noncommutative Field Theories
• $\kappa$-deformed Dirac Equation
• Dynamical symmetries in noncommutative theories
• On general properties of Lorentz invariant formulation of noncommutative quantum field theory
• Quantum complex scalar fields and noncommutativity
• Self-quartic interaction for a scalar field in an extended DFR noncommutative spacetime
• Quantisation of Klein-Gordon field in $\kappa$ space-time: deformed oscillators and Unruh effect
• Quantisation of $\kappa$-deformed Dirac equation

Cited by in corpus (2)

• Maximal acceleration in a Lorentz invariant non-commutative space-time
• $\kappa$-deformed power spectrum and modified Unruh temperature