Abstract
In this paper we consider a two component scalar field theory, with noncommutativity in its conjugate momentum space. We quantize such a theory in a compact space with the help of dressing transformations and we reveal a significant effect of introducing such noncommutativity as the splitting of the energy levels of each individual mode that constitutes the whole system. We further compute the thermal partition function exactly with predicted deformed dispersion relations from noncommutative theories and compare the results with usual results. It is found that thermodynamic quantities in noncommutative models, irrespective of whether the model is more deformed in infrared/UV region, show deviation from standard results in high temperature region.
Highlights
It is a common concept that the usual picture of spacetime as a smooth pseudo-Riemannian manifold would break down due to quantum gravity effects at very short distances of the order of the Planck length
In this paper we have canonically quantized a noncommutative scalar field theory in a compact space with noncommutativity in momentum space following the seminal work of Balachandran et al.[16]
As a result of this noncommutativity, we have noticed the splitting of the energy levels of each individual mode that constitutes the whole system
Summary
It is a common concept that the usual picture of spacetime as a smooth pseudo-Riemannian manifold would break down due to quantum gravity effects at very short distances of the order of the Planck length. After constructing the Hamiltonian formulation of this theory and quantizing it in a compact space, Balachandran et al have obtained a splitting of the energy levels of each individual mode that constitutes the whole system. The resemblance of this effect to the well known Zeeman effect in a quantum system in the presence of a magnetic field is noticed[16]. We canonically quantize a free massless boson theory with the commutation relation in Eq 3 in (1 + 1) dimension following the regularization procedure shown in the seminal paper of Balachandran et al.[16]. We compute the thermal partition function for the deformed Hamiltonian due to noncommutativity in Eq (2) and (3) and compare them
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