arXiv subjects

A. P. Balachandran

Publications and source records attributed to A. P. Balachandran.

At least 55 records · Page 3Linked to original sources

arXiv2012

Quantum Physics and Fluctuating Topologies: Survey

The spin-statistics connection, quantum gravity and other physical considerations suggest that classical space-time topology is not an immutable attribute and can change in quantum physics. The implementation of topology change using quantum principles has been studied for over two decades by a few of us. There has been a recent revival of interest in some of our work, dating back to as early as 1995. The present paper is meant as a resource article to our major relevant papers. It contains summaries of the contents of the cited papers and the corresponding links wherever available.

hep-th↗

arXiv2012

Entanglement, Particle Identity and the GNS Construction: A Unifying Approach

A novel approach to entanglement, based on the Gelfand-Naimark-Segal (GNS) construction, is introduced. It considers states as well as algebras of observables on an equal footing. The conventional approach to the emergence of mixed from pure ones based on taking partial traces is replaced by the more general notion of the restriction of a state to a subalgebra. For bipartite systems of nonidentical particles, this approach reproduces the standard results. But it also very naturally overcomes the limitations of the usual treatment of systems of identical particles. This GNS approach seems very general and can be applied for example to systems obeying para- and braid- statistics including anyons.

quant-ph↗

arXiv2012

Electric Dipole Moment from QCD $θ$ and How It Vanishes for Mixed States

In a previous paper [1], we studied the $η'$ mass and formulated its chirally symmetric coupling to fermions which induces electric dipole moment (EDM). Here we calculate the EDM to one-loop. It is finite, having no ultraviolet divergence while its infrared divergence is canceled by soft photon emission processes \emph{exactly} as for $θ=0$. The coupling does not lead to new divergences (not present for $\sinθ=0$) in soft photon processes either. Furthermore, as it was argued previously [1], the EDM vanishes if suitable mixed quantum states are used. This means that in a quantum theory based on such mixed states, a strong bound on EDM will not necessarily lead to a strong bound such as $|\sin θ|\lesssim 10^{-11}$ . This fact eliminates the need to fine-tune $θ$ or for the axion field.

hep-th↗

arXiv2012

Novel Studies on the η' Effective Lagrangian

The effective Lagrangian for η' incorporating the effect of the QCD θ-angle has been developed previously. We revisit this Lagrangian and carry out its canonical quantization with particular attention to the test function spaces of constraints and the topology of the η'-field. In this way, we discover a new chirally symmetric coupling of this field to chiral multiplets which involves in particular fermions. This coupling violates P and T symmetries. In a subsequent paper, we will evaluate its contribution to the electric dipole moment (EDM) of fermions. Our motivation is to test whether the use of mixed states restores P and T invariance, so that EDM vanishes. This calculation will be shown to have striking new physical consequences.

hep-ph↗

arXiv2012

Mixed States from Anomalies

There are several instances where quantum anomalies of continuous and discrete classical symmetries play an important role in fundamental physics. Examples come from chiral anomalies in the Standard Model of fundamental interactions and gravitational anomalies in string theories. Their generic origin is the fact that classical symmetries may not preserve the domains of quantum operators like the Hamiltonian. In this work, we show by simple examples that anomalous symmetries can often be implemented at the expense of working with mixed states having non-zero entropies. In particular there is the result on color breaking by non-abelian magnetic monopoles. This anomaly can be rectified by using impure states. We also argue that non-abelian groups of twisted bundles are always anomalous for pure states sharpening an earlier argument of Sorkin and Balachandran. This is the case of mapping class groups of geons indicating that "large" diffeos are anomalous for pure states in the presence of geons. Nevertheless diffeo invariance may be restored by using impure states. This work concludes with examples of these ideas drawn from molecular physics. The above approach using impure states is entirely equivalent to restricting all states to the algebra of observables invariant under the anomalous symmetries. For anomalous gauge groups such as color, this would mean that we work with observables singlet under global gauge transformations. For color, this will mean that we work with color singlets, a reasonable constraint.

hep-th↗

arXiv2011

Quantum Gravity: Mixed States from Diffeomorphism Anomalies

In a previous paper, we discussed simple examples like particle on a circle and molecules to argue that mixed states can arise from anomalous symmetries. This idea was applied to the breakdown (anomaly) of color SU(3) in the presence of non-abelian monopoles. Such mixed states create entropy as well. In this article, we extend these ideas to the topological geons of Friedman and Sorkin in quantum gravity. The "large diffeos" or mapping class groups can become anomalous in their quantum theory as we show. One way to eliminate these anomalies is to use mixed states, thereby creating entropy. These ideas may have something to do with black hole entropy as we speculate.

hep-th↗

arXiv2011

Lehmann-Symanzik-Zimmermann S-Matrix elements on the Moyal Plane

Field theories on the Groenewold-Moyal(GM) plane are studied using the Lehmann-Symanzik-Zimmermann(LSZ) formalism. The example of real scalar fields is treated in detail. The S-matrix elements in this non-perturbative approach are shown to be equal to the interaction representation S-matrix elements. This is a new non-trivial result: in both cases, the S-operator is independent of the noncommutative deformation parameter $θ_{μν}$ and the change in scattering amplitudes due to noncommutativity is just a time delay. This result is verified in two different ways. But the off-shell Green's functions do depend on $θ_{μν}$. In the course of this analysis, unitarity of the non-perturbative S-matrix is proved as well.

hep-th↗

arXiv2011

Quantum Geons and Noncommutative Spacetimes

Physical considerations strongly indicate that spacetime at Planck scales is noncommutative. A popular model for such a spacetime is the Moyal plane. The Poincarè group algebra acts on it with a Drinfel'd-twisted coproduct. But the latter is not appropriate for more complicated spacetimes such as those containing the Friedman-Sorkin (topological) geons. They have rich diffeomorphism groups and in particular mapping class groups, so that the statistics groups for N identical geons is strikingly different from the permutation group $S_N$. We generalise the Drinfel'd twist to (essentially) generic groups including to finite and discrete ones and use it to modify the commutative spacetime algebras of geons as well to noncommutative algebras. The latter support twisted actions of diffeos of geon spacetimes and associated twisted statistics. The notion of covariant fields for geons is formulated and their twisted versions are constructed from their untwisted versions. Non-associative spacetime algebras arise naturally in our analysis. Physical consequences, such as the violation of Pauli principle, seem to be the outcomes of such nonassociativity. The richness of the statistics groups of identical geons comes from the nontrivial fundamental groups of their spatial slices. As discussed long ago, extended objects like rings and D-branes also have similar rich fundamental groups. This work is recalled and its relevance to the present quantum geon context is pointed out.

hep-th↗

arXiv2010

Non-Pauli Effects from Noncommutative Spacetimes

Noncommutative spacetimes lead to nonlocal quantum field theories (qft's) where spin-statistics theorems cannot be proved. For this reason, and also backed by detailed arguments, it has been suggested that they get corrected on such spacetimes leading to small violations of the Pauli principle. In a recent paper \cite{Pauli}, Pauli-forbidden transitions from spacetime noncommutativity were calculated and confronted with experiments. Here we give details of the computation missing from this paper. The latter was based on a spacetime $\mathcal{B}_{χ\vec{n}}$ different from the Moyal plane. We argue that it quantizes time in units of $χ$. Energy is then conserved only mod $\frac{2π}χ$. Issues related to superselection rules raised by non-Pauli effects are also discussed in a preliminary manner.

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arXiv2010

Thermofield dynamics and twisted Poincaré symmetry on Moyal space-time

On Moyal space-time, one can implement twisted Poincaré symmetry with the resultant modification of symmetrization and anti-symmetrization postulates for bosons and fermions. We develop the thermofield approach of Umezawa and Takahashi on such a spacetime preserving the twisted Poincaré symmetry of the underlying quantum field theory(qft). Implications of this twisted Poincaré symmetry for qft's at finite temperature are pointed out.

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arXiv2010

Covariant Quantum Fields on Noncommutative Spacetimes

A spinless covariant field $ϕ$ on Minkowski spacetime $\M^{d+1}$ obeys the relation $U(a,Λ)ϕ(x)U(a,Λ)^{-1}=ϕ(Λx+a)$ where $(a,Λ)$ is an element of the Poincaré group $\Pg$ and $U:(a,Λ)\to U(a,Λ)$ is its unitary representation on quantum vector states. It expresses the fact that Poincaré transformations are being unitary implemented. It has a classical analogy where field covariance shows that Poincaré transformations are canonically implemented. Covariance is self-reproducing: products of covariant fields are covariant. We recall these properties and use them to formulate the notion of covariant quantum fields on noncommutative spacetimes. In this way all our earlier results on dressing, statistics, etc. for Moyal spacetimes are derived transparently. For the Voros algebra, covariance and the *-operation are in conflict so that there are no covariant Voros fields compatible with *, a result we found earlier. The notion of Drinfel'd twist underlying much of the preceding discussion is extended to discrete abelian and nonabelian groups such as the mapping class groups of topological geons. For twists involving nonabelian groups the emergent spacetimes are nonassociative.

hep-th↗

arXiv2010

Inequivalence of QFT's on Noncommutative Spacetimes: Moyal versus Wick-Voros

In this paper, we further develop the analysis started in an earlier paper on the inequivalence of certain quantum field theories on noncommutative spacetimes constructed using twisted fields. The issue is of physical importance. Thus it is well known that the commutation relations among spacetime coordinates, which define a noncommutative spacetime, do not constrain the deformation induced on the algebra of functions uniquely. Such deformations are all mathematically equivalent in a very precise sense. Here we show how this freedom at the level of deformations of the algebra of functions can fail on the quantum field theory side. In particular, quantum field theory on the Wick-Voros and Moyal planes are shown to be inequivalent in a few different ways. Thus quantum field theory calculations on these planes will lead to different physics even though the classical theories are equivalent. This result is reminiscent of chiral anomaly in gauge theories and has obvious physical consequences. The construction of quantum field theories on the Wick-Voros plane has new features not encountered for quantum field theories on the Moyal plane. In fact it seems impossible to construct a quantum field theory on the Wick-Voros plane which satisfies all the properties needed of field theories on noncommutative spaces. The Moyal twist seems to have unique features which make it a preferred choice for the construction of a quantum field theory on a noncommutative spacetime.

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arXiv2010

Non-Pauli Transitions From Spacetime Noncommutativity

There are good reasons to suspect that spacetime at Planck scales is noncommutative. Typically this noncommutativity is controlled by fixed "vectors" or "tensors" with numerical entries. For the Moyal spacetime, it is the antisymmetric matrix $θ_{μν}$. In approaches enforcing Poincaré invariance, these deform or twist the method of (anti-)symmetrization of identical particle state vectors. We argue that the earth's rotation and movements in the cosmos are "sudden" events to Pauli-forbidden processes. They induce (twisted) bosonic components in state vectors of identical spinorial particles in the presence of a twist. These components induce non-Pauli transitions. From known limits on such transitions, we infer that the energy scale for noncommutativity is $\gtrsim 10^{24}\textrm{TeV}$. This suggests a new energy scale beyond Planck scale.

hep-th↗

arXiv2010

Poincare' Quasi-Hopf Symmetry and Non-Associative Spacetime Algebra from Twisted Gauge Theories

In previous work, starting from the Moyal plane, we formulated interacting theories of matter and gauge fields with only the former fields twisted. In this approach, gauge theories, including the standard model, can be formulated without new gauge degrees of freedom. We show their underlying symmetry algebra to be Poincaré quasi-Hopf . The associated spacetime algebra is hence non-associative.

hep-th↗

arXiv2009

QED on the Groenewold Moyal Plane

We investigate a version of noncommutative QED where the interaction term, although natural, breaks the spin-statistics connection. We calculate $e^- + e^- -> e^- + e^-$ and $γ+ e^- -> γ+ e^-$ cross-sections in the tree approximation and explicitly display their dependence on theta^{μν}. Remarkably the zero of the elastic $e^- + e^- -> e^- + e^-$ cross-section at 90-degrees in the center-of-mass system, which is due to Pauli principle, is shifted away as a function of theta^{μν} and energy.

hep-th↗

arXiv2009

The Groenewold - Moyal Plane and its Quantum Physics

Quantum theories constructed on the noncommutative spacetime called the Groenewold-Moyal(GM) plane exhibit many interesting properties such as causality violation, Lorentz and CPT non-invariance and twisted statistics. Such violations lead to many striking features that may be tested experimentally. Thus these theories predict Pauli-forbidden transitions due to twisted statistics, anisotropies and acausal effects in the cosmic microwave background radiation in correlations of observables and Lorentz and CPT violations in scattering amplitudes. Such features of quantum physics on the GM plane are surveyed in this review.

hep-th↗

arXiv2009

Spin $j$ Dirac Operators on the Fuzzy 2-Sphere

The spin 1/2 Dirac operator and its chirality operator on the fuzzy 2-sphere $S^2_F$ can be constructed using the Ginsparg-Wilson(GW) algebra [arxiv:hep-th/0511114]. This construction actually exists for any spin $j$ on $S^2_F$, and have continuum analogues as well on the commutative sphere $S^2$ or on $\mathbb{R}^{2}$. This is a remarkable fact and has no known analogue in higher dimensional Minkowski spaces. We study such operators on $S^2_F$ and the commutative $S^2$ and formulate criteria for the existence of the limit from the former to the latter. This singles out certain fuzzy versions of these operators as the preferred Dirac operators. We then study the spin 1 Dirac operator of this preferred type and its chirality on the fuzzy 2-sphere and formulate its instanton sectors and their index theory. The method to generalize this analysis to any spin $j$ is also studied in detail.

hep-th↗

arXiv2009

Finite Temperature Field Theory on the Moyal Plane

In this paper, we initiate the study of finite temperature quantum field theories (QFT's) on the Moyal plane. Such theories violate causality which influences the properties of these theories. In particular, causality influences the fluctuation-dissipation theorem: as we show, a disturbance in a space-time region $M_1$ creates a response in a space-time region $M_2$ space-like with respect to $M_1$ ($M_1\times M_2$). The relativistic Kubo formula with and without noncommutativity is discussed in detail, and the modified properties of relaxation time and the dependence of mean square fluctuations on time are derived. In particular, the Sinha-Sorkin result \cite{sorkin-sinha} on the logarithmic time dependence of the mean square fluctuations is discussed in our context. We derive an exact formula for the noncommutative susceptibility in terms of the susceptibility for the corresponding commutative case. It shows that noncommutative corrections in the four-momentum space have remarkable periodicity properties as a function of the four-momentum $k$. They have direction dependence as well and vanish for certain directions of the spatial momentum. These are striking observable signals for noncommutativity. The Lehmann representation is also generalized to any value of the noncommutativity parameter $θ^{μν}$ and finite temperatures.

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