arXiv subjects

A. P. Balachandran

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

At least 19 recordsLinked to original sources

arXiv2024

Asymptotic Quantization of Palatini Action

The Palatini action is based on vector-valued one forms or frames and SL(2,C) connections on R^4. Using the spacetime split of R^4 as a direct sum of R^3 and R^1, the Gauss law in this paper is treated on a Hilbert space. This is achieved by noting that quantum operators act on a complex Hilbert space and SL(2,C) is just the complexification of the compact SU(2) in the self-dual (1/2,0) representation used for the Ashtekar variables. This observation enables a treatment of small and large gauge transformations and superselection sectors. An explicit representation of theta vacua and their attendant 'spin-isospin mixing' are also shown. It is argued that the Gauss law algebra replaces that of diffeomorphisms in the Palatini approach : operators implementing the latter with the correct algebraic relations do not seem available. (Those obtained by multiplying Gauss law operators with fields do not have the correct commutators.)

gr-qc↗

arXiv2024

Confinement and Deconfinement in Gauge Theories: A Quantum Field Theory

After a brief recount of small and large gauge transformations and the nature of observables, we discuss superselection sectors in gauge theories. There are an infinity of them, classified by large gauge transformations. Gauge theory sectors are labelled by the eigenvalues of a complete commuting set (CCS) of these transformations. In QED, the standard chemical potential is one such operator generating global U(1). There are many more given by the moments of the electric field on the sphere at infinity. In QCD, the CCS are constructed from the two commuting generators spanning a Cartan subalgebra. Large gauge transformations commute with the Hamiltonian and preserve the equations of motion. They form an infinite number of `classical symmetries'. But most of them are anamolous changing the superselection sectors. We show that any element of a large gauge transformation can be added to the standard Hamiltonian as a generalised chemical potential without changing field equations and that in QCD, they lead to confined and deconfined phases . A speculation about the physical meaning of these chemical potentials is also made.

hep-th↗

arXiv2024

A Non-Abelian Gauge Theory for Surface Excitations of $~^3$He-B

In $~^3$He-B, two atoms pair in an orbital angular momentum $1$ spin triplet state above the phase transition temperature with $SO(3) \times SO(3)$ symmetry. Below the transition temperature, this symmetry is spontaneously broken to the diagonal $SO(3)$ due to spin-orbit coupling. Considerations based on effective potentials and solitons show that $SO(3)$'s gets enhanced to $SU(3)$'s and the symmetry breaking is that of $G= SU(3) \times SU(3)\times U(1)$ to $H= SU(3)$. The theory of the resultant Goldtsone modes can be naturally formulated as a gauge theory of $H$. Its Gauss law is treated here and shown to lead to surface states in a container with a dynamics governed by large gauge transformations. Observable consequences are pointed. The transference of the analysis to the chiral model of QCD is pointed out where $SU(3)$ are the left and right chiral groups, $U(1)$ is the axial $U(1)$ , the surviving symmetry is flavour $SU(3)$ and the Goldstone modes are the pions.

hep-th↗

arXiv2024

Disorder-free localisation in continuous-time quantum walks : Role of symmetries

We investigate the phenomenon of disorder-free localisation in quantum systems with global permutation symmetry. We use permutation group theory to systematically construct permutation symmetric many-fermion Hamiltonians and interpret them as generators of continuous-time quantum walks. When the number of fermions is very large we find that all the canonical basis states localise at all times, without the introduction of any disorder coefficients. This time-independent localisation is not the result of any emergent disorder distinguishing it from existing mechanisms for disorder-free localisation. Next we establish the conditions under which the localisation is preserved. We find that interactions that preserve and break the global permutation symmetry sustains localisation. Furthermore the basis states of systems with reduced permutation symmetry, localise even for a small number of fermions when the symmetry-reducing parameters are tuned accordingly. We show that similar localisation also occurs for a permutation symmetric Heisenberg spin chain and permutation symmetric bosonic systems, implying that the localisation is independent of the superselected symmetry. Finally we make connections of the Hamiltonians studied here to the adjacency matrices of graphs and use this to propose a prescription for disorder-free localisation in continuous-time quantum walk systems. Many of the models proposed here feature all-to-all connectivity and can be potentially realised on superconducting quantum circuits, trapped ion systems and ultracold atoms.

quant-ph↗

arXiv2023

Violation of the Landau-Yang theorem from Infrared Lorentz Symmetry Breaking

Lorentz symmetry forbids decays of massive spin-1 particle like the $Z^0$ into two massless photons, a result known as the Landau-Yang theorem. But it is known that infrared effects can break Lorentz invariance. Employing the construction of Mund et. al. \cite{MRS} which incorporated this Lorentz violation, we propose an interaction leading to the decay $Z^0 \rightarrow 2 γ$ and study the dependence of the decay on the parameter of this Lorentz violation.

hep-ph↗

arXiv2023

Spin 1/2 from Gluons

The theta vacuum in QCD is the standard vacuum, twisted by the exponential of the Chern-Simons term. But what is the quantum operator $U(g)$ for winding number $1$? We construct $U(g)$ in this note. The Poincare' rotation generators commute with it only if they are augmented by the spin 1/2 representation of the Lorentz group coming from large gauge transformations. This result is analogous to the 'spin-isopin' mixing result due to Jackiw and Rebbi [1], and Hasenfratz and 't Hooft[2] and a similar result in fuzzy physics [3]. Hence states can drastically affect representations of observables. This fact is further shown by charged states dressed by infrared clouds. Following Mund, Rehren and Schroer [4], we find that Lorentz invariance is spontaneously broken in these sectors. This result has been extended earlier to QCD (references [15] given in the Final Remarks) where even the global QCD group is shown to be broken. It is argued that the escort fields of [4] are the Higgs fields for Lorentz and colour breaking. They are string-localised fields where the strings live in a union of de Sitter spaces. Their oscillations and those of the infrared clouds generate the associated Goldstone modes.

hep-th↗

arXiv2022

Review of Twisted Poincare Symmetry

This article reviews the construction and some applications of twisted Poincare-covariant quantum fields on the Moyal plane. The Drinfeld twist, which plays a key mathematical role in this construction, is then applied to the case of discrete groups, with a view to applications to geons in quantum gravity. The Poincare-twisted fields can also be applied to study the CMB anisotropies, and corrections to the power spectrum are used to put constraints on spacetime noncommutativity. The article also addresses the issue of the difference between Moyal and Voros quantum fields. Finally, it is pointed out that the Euclidean functional integrals of QFTs on the Moyal plane do not, in general, obey reflection positivity.

hep-th↗

arXiv2021

Superselection, Boundary Algebras and Duality in Gauge Theories

We consider the generators of gauge transformations with test functions which do not vanish on the boundary of a spacelike region of interest. These are known to generate the edge degrees of freedom in a gauge theory. In this paper, we augment these by introducing the dual or magnetic analogue of such operators. We then study the algebra of these operators, focusing on implications for the superselection sectors of the gauge theory. A manifestly duality-invariant action is also considered, from which alternate descriptions which are $SL(2, \mathbb{Z})$ transforms of each other can be obtained. We also comment on a number of issues related to local charges, definition of confinement and the appearance of interesting mathematical structures such as the Drinfel'd double and the Manin triple.

hep-th↗

arXiv2021

Uncertainties in Quantum Measurements: A Quantum Tomography

The observables associated with a quantum system $S$ form a non-commutative algebra ${\mathcal A}_S$. It is assumed that a density matrix $ρ$ can be determined from the expectation values of observables. But $\mathcal A_S$ admits inner automorphisms $a\mapsto uau^{-1},\; a,u\in {\mathcal A}_S$, $u^*u=u^*u=1$, so that its individual elements can be identified only up to unitary transformations. So since $\mathrm{Tr} ρ(uau^*)= \mathrm{Tr} (u^*ρu)a$, only the spectrum of $ρ$, or its characteristic polynomial, can be determined in quantum mechanics. In local quantum field theory, $ρ$ cannot be determined at all, as we shall explain. However, abelian algebras do not have inner automorphisms, so the measurement apparatus can determine mean values of observables in abelian algebras ${\mathcal A}_M\subset {\mathcal A}_S$ ($M$ for measurement, $S$ for system). We study the uncertainties in extending $ρ|_{{\mathcal A}_M}$ to $ρ|_{{\mathcal A}_S}$ (the determination of which means measurement of ${\mathcal A}_S$) and devise a protocol to determine $ρ|_{{\mathcal A}_S}\equiv ρ$ by determining $ρ|_{{\mathcal A}_M}$ for different choices of ${\mathcal A}_M$. The problem we formulate and study is a generalization of the Kadison-Singer theorem. We give an example where the system $S$ is a particle on a circle and the experiment measures the abelian algebra of a magnetic field $B$ coupled to $S$. The measurement of $B$ gives information about the state $ρ$ of the system $S$ due to operator mixing. Associated uncertainty principles for von Neumann entropy are discussed in the appendix, adapting the earlier work of Białynicki-Birula and Mycielski to the present case.

quant-ph↗

arXiv2020

The Gauss Law: A Tale

The Gauss law plays a basic role in gauge theories, enforcing gauge invariance and creating edge states and superselection sectors. This article surveys these aspects of the Gauss law in QED, QCD and nonlinear $G/H$ models. It is argued that nonabelian superselection rules are spontaneously broken. That is the case with $SU(3)$ of colour which is spontaneously broken to $U(1)\times U(1)$. Nonlinear $G/H$ models are reformulated as gauge theories and the existence of edge states and superselection sectors in these models is also established.

hep-th↗

arXiv2019

Aspects of Boundary Conditions for Nonabelian Gauge Theories

The boundary values of the time-component of the gauge potential form externally specifiable data characterizing a gauge theory. We point out some consequences such as reduced symmetries, bulk currents for manifolds with disjoint boundaries and some nuances of how the charge algebra is realized.

hep-th↗

arXiv2019

Emergent Gauge Symmetries and Quantum Operations

The algebraic approach to quantum physics emphasizes the role played by the structure of the algebra of observables and its relation to the space of states. An important feature of this point of view is that subsystems can be described by subalgebras, with partial trace being replaced by the more general notion of restriction to a subalgebra. This, in turn, has recently led to applications to the study of entanglement in systems of identical particles. In the course of those investigations on entanglement and particle identity, an emergent gauge symmetry has been found by Balachandran, de Queiroz and Vaidya. In this letter we establish a novel connection between that gauge symmetry, entropy production and quantum operations. Thus, let A be a system described by a finite dimensional observable algebra and $ω$ a mixed faithful state. Using the Gelfand-Naimark-Segal (GNS) representation we construct a canonical purification of $ω$, allowing us to embed A into a larger system C. Using Tomita-Takasaki theory, we obtain a subsystem decomposition of C into subsystems A and B, without making use of any tensor product structure. We identify a group of transformations that acts as a gauge group on A while at the same time giving rise to entropy increasing quantum operations on C. We provide physical means to simulate this gauge symmetry/quantum operation duality.

quant-ph↗

arXiv2018

Near-horizon modes and self-adjoint extensions of the Schroedinger operator

We investigate the dynamics of scalar fields in the near-horizon exterior region of a Schwarzschild black hole. We show that low-energy modes are typically long-living and might be considered as being confined near the black hole horizon. Such dynamics are effectively governed by a Schroedinger operator with infinitely many self-adjoint extensions parameterized by $U(1)$, a situation closely resembling the case of an ordinary free particle moving on a semiaxis. Even though these different self-adjoint extensions lead to equivalent scattering and thermal processes, a comparison with a simplified model suggests a physical prescription to chose the pertinent self-adjoint extensions. However, since all extensions are in principle physically equivalent, they might be considered in equal footing for statistical analyses of near-horizon modes around black holes. Analogous results hold for any non-extremal, spherically symmetric, asymptotically flat black hole.

gr-qc↗

arXiv2018

Entangled Scent of a Charge

We argue that the ground state of a field theory, in the presence of charged particles, becomes an entangled state involving an infinity of soft photons. The quantum field vacuum is altered by the passage of a uniformly moving charge, leaving in its wake a different dressed ground state. In this sense a charged particle leaves its electromagnetic scent even after passing by. Unlike in classical electrodynamics the effect of the charge remains even at infinite time. The calculation is done in detail for the ground state of a spacetime wedge, although the results are more general. This agrees in spirit with recent results over the infrared aspects of field theory, although the technical details are different. These considerations open the possibility that the information carried by quantum fields, being nonlocal, does not disappear beyond the horizon of black holes.

hep-th↗

arXiv2018

Novel Edge States in Self-Dual Gravity

In contrast to the Einstein-Hilbert action, the action for self-dual gravity contains vierbeins. They are eleminated at the level of observables by an $SL(2,\mathbb{C})$ gauge condition implied by the action. We argue that despite this condition, new "edge" or superselected state vectors corresponding to maps of the spheres $S^2_{\infty}$ at infinity to $SL(2, \mathbb{C})$ arise. They are characterised by new quantum numbers and they lead to mixed states. For black holes, they arise both at the horizon and the spatial infinity and may be relevant for the black hole information paradox. Similar comments can be made about the Einstein-Palatini action which uses vierbeins.

hep-th↗

arXiv2018

An Action for the Infrared Regime of Gauge Theories and the Problem of Color Transformations

It has been known for a while that there is spontaneous breaking of Lorentz symmetry in the nonzero charged sectors of quantum electrodynamics due to the infrared problem of soft photons. More recently, it has also been suggested that similar results hold for color transformations in a nonabelian gauge theory. Here we show that an action where a diffeomorphism has been carried out for the part describing hard gauge particles and matter fields can be used to analyze these issues. In addition to rederiving old results in this formalism, we also show that color transformations cannot be unitarily implemented on perturbative gluon states if gluon fields of arbitrarily low energy are allowed. Implications for confinement and mass gap are briefly commented upon.

hep-th↗

arXiv2017

Matrix Model of QCD: Edge Localized Glue Balls and Phase Transitions

In a matrix model of pure $SU(2)$ Yang-Mills theory, boundaries emerge in the space of $\textrm{Mat}_{3}(\mathbb{R})$ and the Hamiltonian requires boundary conditions. We show the existence of edge localized glueball states which can have negative energies. These edge levels can be lifted to positive energies if the gluons acquire a London-like mass. This suggests a new phase of QCD with an incompressible bulk.

hep-th↗

arXiv2017

Localization in the Rindler Wedge

One of the striking features of QED is that charged particles create a coherent cloud of photons. The resultant coherent state vectors of photons generate a non-trivial representation of the localized algebra of observables that do not support a representation of the Lorentz group: Lorentz symmetry is spontaneously broken. We show in particular that Lorentz boost generators diverge in this representation, a result shown also in [1] (See also [2]). Localization of observables, for example in the Rindler wedge, uses Poincaré invariance in an essential way [3]. Hence in the presence of charged fields, the photon observables cannot be localized in the Rindler wedge. These observations may have a bearing on the black hole information loss paradox, as the physics in the exterior of the black hole has points of resemblance to that in the Rindler wedge.

hep-th↗