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Gordon W. Semenoff

Publications and source records attributed to Gordon W. Semenoff.

At least 19 recordsLinked to original sources
arXiv2026

The Wilson-line-dressed charged sector of scalar QED: superselection and the infraparticle

We develop a manifestly gauge and Lorentz invariant perturbative calculus to study the finite time and distance evolution of the electrically charged states created by Wilson-line-dressed scalar field operators in scalar quantum electrodynamics. By an Osterwalder-Schrader reflection and Euclidean gluing, the overlap of two dressed states is expressed as a Euclidean 2 point function of dressed operators, which is then evaluated in renormalized perturbation theory with a Stueckelberg photon mass as a gauge, BRST and Lorentz invariant infrared cutoff. This renders explicit and computable in closed form several structural features of the charged sector that have so far been accessible mainly through non-perturbative or algebraic arguments. We find that states dressed by non-parallel Wilson lines are ``cloud orthogonal". Their overlap vanishes as a power of the infrared regulator, with an exponent that depends only on the angle between the two dressings and is an infrared analogue of the cusp anomalous dimension with the difference that it is one-loop exact whenever the charged matter is mass-gapped. Charged states are thereby superselected by the orientation of their dressing. Within a superselection sector the 2 point function is infrared finite but exhibits the infraparticle. The mass shell pole is replaced by the edge of a branch cut. As a result, the asymptotic spread of a dressed charge is a power law in proper time with a one-loop-exact computable exponent depending on the dressing and on the direction of motion. We show that although cloud orthogonality and the infraparticle are each extremely sensitive to fundamental infrared cutoffs, the infraparticle scaling law persists across a wide window of proper time.

hep-th↗
arXiv2025

Entropy from scattering in weakly interacting systems

Perturbation theory is used to investigate the evolution of the von Neumann entropy of a subsystem of a bipartite quantum system under the action of a unitary matrix, in the limit where that matrix is close to the unit matrix. The physical context for such process would be scattering with weak short-ranged interactions where the unitary matrix is the S matrix. We find surprisingly simple criteria for the initial state and the S matrix that guarantee that the subsystem entropy increases. The class of initial states that meet these criteria are more correlated than simple product states of the subsystems. They form a subclass of the set of all separable states, and they can therefore be assembled by classical processes alone.

quant-ph↗
arXiv2024

Parity Violating Marginal Deformation of the 3D Gross-Neveu-Thirring Model

A hybrid of the critical three dimensional Gross-Neveu and Thirring models deformed by explicit parity breaking operators is studied in the large N expansion and using the renormalization group. The regime of coupling constants where the theory is stable is identified and criteria for the occurrence of fixed points in that regime are found. For a certain range of Chern-Simons level, we find stable charge-gapped phase with spontaneously broken approximate scale invariance and a parametrically light dilaton. The Chern-Simons level can be tuned to the stability edge resulting in exact scale invariance which is spontaneously broken, accompanied by a massless dilaton. For another, narrow range of Chern-Simons levels we find a conformal window where the theory flows to a Wilson-Fisher-like fixed point and is a novel (and rare) example of a non-supersymmetric non-trivial parity and time reversal violating three dimensional conformal field theory with scalar, spinor and vector fields.

hep-th↗
arXiv2024

Scale Invariance at the Edge

Some aspects of the theory of fermions living on three dimensional spacetime with a flat co-dimension one boundary are discussed, particularly a case where the boundary condition preserves scale and translation invariance but violates the residual Lorentz and conformal symmetries. This case is interesting because the Dirac equation has normalizable stationary edge states which must be taken into account in the quantization. We show that a consequence of the edge states for quantization of the Dirac field is that there are no states of the Dirac field theory which are simultaneously scale, C and P invariant even when these are good symmetries of the theory. The scale invariant states of the Dirac field contain either a nonzero scale covariant momentum density or a U(1) charge density concentrated near the edge.

hep-th↗
arXiv2024

Dilaton in a Multicritical 3+epsilon-D Parity Violating Field Theory

The multi-critical behaviour of an approximately scale and conformal invariant quantum field theory, which can be regarded as the deformation of the critical Gross-Neveu model in 3+epsilon dimensions by a nearly marginal parity violating operator, is studied using a large $N$ expansion. When epsilon is greater than a number of order 1/N, the deformation is marginally relevant and it is found to exhibit spontaneous breaking of the approximate scale symmetry accompanied by the appearance of a light scalar in its spectrum. The scalar mass is parametrically small, of order epsilon times the fermion mass and it can be identified with a light dilaton. When the dimension is reduced to 3 the deformation of the Gross-Neveu model becomes marginally irrelevant, what was a minimum of the potential becomes a maximum and the theory has a non-perturbative global instability. There is a metastable perturbative phase where the scalar does not condense and the fermions are massless separated by an energy barrier with height of order one (rather than N) from an energetically favoured phase with a runaway condensate.

hep-th↗
arXiv2022

Boundary Ferromagnetism in Zigzag Edged Graphene

The flat band of edge states which occur in the simple tight-binding lattice model of graphene with a zig-zag edge have long been conjectured to take up a ferromagnetic configuration. In this work we demonstrate that, for a large class of interaction Hamiltonians which can be added to the tight-binding model, and at the first order in perturbation theory, the degeneracy of the edge states is resolved in such a way that the ground state is in the maximal, spin j = N/2 representation of the spin symmetry where N is the number of edge states.

cond-mat.mes-hall↗
arXiv2022

Soft Scalars don't decouple

It is demonstrated that it is possible to find a field theory containing massless scalar particles which has infrared structure closely resembling that of quantum electrodynamics and perturbative quantum gravity but exhibiting no gauge invariance or internal symmetries at all, and in particular, no apparent asymptotic symmetry. It is shown that, unlike soft photons and gravitons, the soft scalars do not decouple from dressed states and they are generically produced when hard dressed particles interact. However, the entanglement of the hard and resulting soft particles is vanishingly small.

hep-th↗
arXiv2022

Massless Fermions on a half-space: The curious case of 2+1-dimensions

Boundary conditions for a massless Dirac fermion in 2+1 dimensions where the space is a half-plane are discussed in detail. It is argued that linear boundary conditions that leave the Hamiltonian Hermitian generically break $C$ $P$ and $T$ symmetries as well as Lorentz and conformal symmetry. We show that there is essentially one special case where a single species of fermion has $CPT$ and the full Poincare and conformal symmetry of the boundary. We show that, with doubled fermions, there is a second special case which respects $CPT$ but still violates Lorentz and conformal symmetry. This second special case is essentially the unique boundary condition where the Dirac operator has fermion zero mode edge states. We discuss how the edge states lead to exotic representations of scale, phase and translation symmetries and how imposing a symmetry requirement leads to edge ferromagnetism of the system. We prove that the exotic ferromagnetic representations are indeed carried by the ground states of the system perturbed by a class of interaction Hamiltonians which includes the non-relativistic Coulomb interaction.

hep-th↗
arXiv2020

On the infrared divergence and global colour in N=4 Yang-Mills theory

The N=4 superconformal Yang-Mills theory on flat four-dimensional Minkowski space is a de-confined gauge theory in the sense that the string tension for fundamental representation coloured quarks vanishes. In fact, static fundamental representation quarks which lie in certain half-BPS super-multiplets do not interact at all. An interesting question asks whether such quarks would carry a well-defined global colour charge which, when the gauge is fixed, should have the status of an internal symmetry. We shall present a simple paradigmatic model which suggests that the answer to this question lies in the way in which infrared divergences are dealt with.

hep-th↗
arXiv2020

How to Split the Electron in Half

This essay is a tribute to Professor Roman Jackiw on the occasion of his eightieth year. It discusses some ideas about Fermion zero modes and fractional charges and quantum entanglement.

cond-mat.mes-hall↗
arXiv2019

Entanglement and the Infrared

We shall outline some results regarding the infrared catastrophes of quantum electrodynamics and perturbative quantum gravity and their implications for information loss in quantum processes involving electrically or gravitationally charged particles. We will argue that two common approaches to the solution of the infrared problem, using transition probabilities which are inclusive of copious soft photon and graviton production and using dressed states describe fundamentally different quantizations of electrodynamics and low energy gravity which are, in principle, distinguishable by experiments.

hep-th↗
arXiv2019

Defect QED: Dielectric without a Dielectric, Monopole without a Monopole

We study a class of defect quantum field theories where the quantum field theory in the 3+1-dimensional bulk is a free photon and charged matter and the interactions of the photons with the charges occur entirely on a 2+1-dimensional defect. We observe that at the fully quantum level, the effective action of such a theory is still a defect field theory with free photons propagating in the bulk and the nonlinearities in the quantum corrections to the Maxwell equations confined to the defect. We use this observation to show that the defect field theory has interesting electromagnetic properties. The electromagnetic fields sourced by static test charges are attenuated as if the bulk surrounding them were filled with a dielectric material. This is particularly interesting when the observer and test charge are on opposite sides of the defect. Then the effect is isotropic and it is operative even in the region near the defect. If the defect is in a time reversal violating state, image charges have the appearance of electrically and magnetically charged dyons. We present the example of a single layer in a quantum Hall state. We observe that the charge screening effect in charge neutral graphene should be significant, and even more dramatic when the layer is in a metallic state with mobile electrons.

hep-th↗
arXiv2018

Dilaton in a cold Fermi gas

These are the notes for a lecture which I presented at the International Conference on New Frontiers in Physics in Kolymbari, Crete in July, 2018. They review an idea which posits a phase of a two-dimensional system of cold N-component Fermions which exhibits spontaneously broken approximate scale symmetry when studied in the large N expansion. Near criticality, the phase exhibits anomalously small pressure and large compressibility. Some of the consequences of the approximate scale symmetry, such as the existence of a dilaton and its properties are discussed.

cond-mat.quant-gas↗
arXiv2018

Edge Modes and Teleportation in a Topologically Insulating Quantum Wire

We find a simple model of an insulating state of a quantum wire which has a single isolated edge mode. We argue that, when brought to proximity, the edge modes on independent wires naturally form Bell entangled states which could be used for elementary quantum processes such as teleportation. We give an example of an algorithm which teleports the spin state of an electron from one quantum wire to another.

quant-ph↗
arXiv2018

Dynamical violation of scale invariance and the dilaton in a cold Fermi gas

We use the large N approximation to find an exotic phase of a cold, two-dimensional, N-component Fermi gas which exhibits dynamically broken approximate scale symmetry. We identify a particular weakly damped collective excitation as the dilaton, the pseudo-Goldstone boson associated with the broken approximate scale symmetry. We argue that the symmetry breaking phase is stable for a range of parameters of the theory and there is a fluctuation induced first order quantum phase transition between the normal and the scale symmetry breaking phases which can be driven by tuning the chemical potential. We find that the compressibility of the gas at its lower critical density is anomalously large, 2N times that of a perfect gas at the same density.

cond-mat.quant-gas↗
arXiv2017

Worldsheet Instantons and the amplitude for string pair production in an external field as a WKB exact functional integral

We revisit the problem of charged string pair creation in a constant external electric field. The string states are massive and creation of pairs from the vacuum is a tunnelling process, analogous to the Schwinger process where charged particle-anti-particle pairs are created by an electric field. We find the instantons in the worldsheet sigma model which are responsible for the tunnelling events. We evaluate the sigma model partition function in the multi-instanton sector in the WKB approximation which keeps the classical action and integrates the quadratic fluctuations about the solution. We find that the summation of the result over all multi-instanton sectors reproduces the known amplitude. This suggests that corrections to the WKB limit must cancel. To show that they indeed cancel, we identify a fermionic symmetry of the sigma model which occurs in the instanton sectors and which is associated with collective coordinates. We demonstrate that the action is symmetric and that the interaction action is an exact form. These conditions are sufficient for localization of the worldsheet functional integral onto its WKB limit.

hep-th↗