Pramod Padmanabhan

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 [1], 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

Causality and Statistics on the Groenewold–Moyal Plane

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Spin j Dirac operators on the fuzzy 2-sphere

different from the Moyal plane. We argue that it quantizes time in units of χ. Energy is then conserved only mod

Supersymmetric many-body systems from partial symmetries — integrability, localization and scrambling

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Lehmann-Symanzik-Zimmermann S -matrix elements on the Moyal plane

. Issues related to superselection rules raised by non-Pauli effects are also discussed in a preliminary manner.

The Groenewold—Moyal Plane and its Quantum Physics

Quantum theories constructed on the noncommutative spacetime called the Groenewold–Moyal plane exhibit many interesting properties such as Lorentz and CPT noninvariance, causality violation and twisted statistics. We show that such violations lead to many striking features that may be tested experimentally. These theories predict Pauli forbidden transitions due to twisted statistics, anisotropies in the cosmic microwave background radiation due to correlations of observables in spacelike regions and Lorentz and CPT violations in scattering amplitudes.

Unusual thermodynamics on the fuzzy 2-sphere

The spin ½ Dirac operator and its chirality operator on the fuzzy 2-sphere S2F can be constructed using the Ginsparg-Wilson (GW) algebra [1]. This construction actually exists for any spin j on S2F, and have continuum analogues as well on the commutative sphere S2 or on 2. This is a remarkable fact and has no known analogue in higher dimensional Minkowski spaces. We study such operators on S2F and the commutative S2 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.

Non-Pauli Transitions from Spacetime Noncommutativity

A bstractPartial symmetries are described by generalized group structures known as symmetric inverse semigroups. We use the algebras arising from these structures to realize supersymmetry in (0+1) dimensions and to build many-body quantum systems on a chain. This construction consists in associating appropriate supercharges to chain sites, in analogy to what is done in spin chains. For simple enough choices of supercharges, we show that the resulting states have a finite non-zero Witten index, which is invariant under perturbations, therefore defining supersymmetric phases of matter protected by the index. The Hamiltonians we obtain are integrable and display a spectrum containing both product and entangled states. By introducing disorder and studying the out-of-time-ordered correlators (OTOC), we find that these systems are in the many-body localized phase and do not thermalize. Finally, we reformulate a theorem relating the growth of the second Rényi entropy to the OTOC on a thermal state in terms of partial symmetries.

A Recipe for Constructing Exactly Soluble Lattice Models with Gauge and Matter Fields in One and Two Dimensions

Field theories on the Groenewold-Moyal plane are studied using the Lehmann-Symanzik-Zimmermann formalism. The example of real scalar fields is treated in detail. The

Realizing the fusion rules of Ising anyons without lattice defects

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