اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدThermal effective potential in two- and three- dimensional non-commutative spaces
42
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Thermal correlation functions and the associated effective statistical potential are computed in two- and three-dimensional non-commutative space using an operator formulation that makes no reference to a star product. The corresponding results for the Moyal and Voros star products are then easily obtained by taking the corresponding overlap with Moyal and Voros bases. The forms of the correlation function and the effective potential are found to be the same, except that in the Voros case the thermal length undergoes a non-commutative deformation, ensuring that it has a lower bound of the order of $sqrt{theta}$. It is shown that in a suitable basis (called here quasi-commutative) in the multi-particle sector the thermal correlation function coincides with the commutative result both in the Moyal and Voros cases, with an appropriate non-commutative correction to the thermal length in the Voros case, and that the Pauli principle is restored.
قيم البحث
اقرأ أيضاً
We discuss 2-cocycles of the Lie algebra $Map(M^3;g)$ of smooth, compactly supported maps on 3-dimensional manifolds $M^3$ with values in a compact, semi-simple Lie algebra $g$. We show by explicit calculation that the Mickelsson-Faddeev-Shatashvili
cocycle $f{ii}{24pi^2}inttrac{Accr{dd X}{dd Y}}$ is cohomologous to the one obtained from the cocycle given by Mickelsson and Rajeev for an abstract Lie algebra $gz$ of Hilbert space operators modeled on a Schatten class in which $Map(M^3;g)$ can be naturally embedded. This completes a rigorous field theory derivation of the former cocycle as Schwinger term in the anomalous Gauss law commutators in chiral QCD(3+1) in an operator framework. The calculation also makes explicit a direct relation of Connes non-commutative geometry to (3+1)-dimensional gauge theory and motivates a novel calculus generalizing integration of $g$-valued forms on 3-dimensional manifolds to the non-commutative case.
We show that it is in principle possible to construct dualities between commutative and non-commutative theories in a systematic way. This construction exploits a generalization of the exact renormalization group equation (ERG). We apply this to the
simple case of the Landau problem and then generalize it to the free and interacting non-canonical scalar field theory. This constructive approach offers the advantage of tracking the implementation of the Lorentz symmetry in the non-commutative dual theory. In principle, it allows for the construction of completely consistent non-commutative and non-local theories where the Lorentz symmetry and unitarity are still respected, but may be implemented in a highly non-trivial and non-local manner.
The effect of non-commutativity on electromagnetic waves violates Lorentz invariance: in the presence of a background magnetic induction field b, the velocity for propagation transverse to b differs from c, while propagation along b is unchanged. In
principle, this allows a test by the Michelson-Morley interference method. We also study non-commutativity in another context, by constructing the theory describing a charged fluid in a strong magnetic field, which forces the fluid particles into their lowest Landau level and renders the fluid dynamics non-commutative, with a Moyal product determined by the background magnetic field.
In this paper, we compute the constrained QCD effective potential up to two-loop order with finite quark mass and chemical potential. We present the explicit calculations by using the double line notation and analytical expressions for massless quark
s are obtained in terms of the Bernoulli polynomials or Polyakov loops. Our results explicitly show that the constrained QCD effective potential is independent on the gauge fixing parameter. In addition, as compared to the massless case, the constrained QCD effective potential with massive quarks develops a completely new term which is only absent when the background field vanishes. Furthermore, we discuss the relation between the one- and two-loop constrained effective potential. The surprisingly simple proportionality that exists in the pure gauge theories, however, is in general no longer true when fermions are taken into account. On the other hand, for high baryon density $mu_B$ and low temperature $T$, in the massless limit, we do also find a similar proportionality between the one- and two-loop fermionic contributions in the constrained effective potential up to ${cal O}(T/mu_B)$.
We revise and extend the algorithm provided in [1] to compute the finite Connes distance between normal states. The original formula in [1] contains an error and actually only provides a lower bound. The correct expression, which we provide here, inv
olves the computation of the infimum of an expression which involves the transverse component of the algebra element in addition to the longitudinal component of [1]. This renders the formula less user-friendly, as the determination of the exact transverse component for which the infimum is reached remains a non-trivial task, but under rather generic conditions it turns out that the Connes distance is proportional to the trace norm of the difference in the density matrices, leading to considerable simplification. In addition, we can determine an upper bound of the distance by emulating and adapting the approach of [2] in our Hilbert-Schmidt operatorial formulation. We then look for an optimal element for which the upper bound is reached. We are able to find one for the Moyal plane through the limit of a sequence obtained by finite dimensional projections of the representative of an element belonging to a multiplier algebra, onto the subspaces of the total Hilbert space, occurring in the spectral triple and spanned by the eigen-spinors of the respective Dirac operator. This is in contrast with the fuzzy sphere, where the upper bound, which is given by the geodesic of a commutative sphere is never reached for any finite $n$-representation of $SU(2)$. Indeed, for the case of maximal non-commutativity ($n = 1/2$), the finite distance is shown to coincide exactly with the above mentioned lower bound, with the transverse component playing no role. This, however starts changing from $n=1$ onwards and we try to improve the estimate of the finite distance and provide an almost exact result, using our new and modified algorithm.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
