Publications

Order by: publication date number of citations

• Quantum simulation of colour in perturbative quantum chromodynamics

  Herschel A. Chawdhry, Mathieu Pellen

  SciPost Phys. 15, 205 (2023) · published 24 November 2023 | Toggle abstract · pdf

  Quantum computers are expected to give major speed-ups for the simulation of quantum systems. In this work, we present quantum gates that simulate the colour part of the interactions of quarks and gluons in perturbative quantum chromodynamics (QCD). As a first application, we implement these circuits on a simulated noiseless quantum computer and use them to calculate colour factors for various examples of Feynman diagrams. This work constitutes a first key step towards a quantum simulation of generic scattering processes in perturbative QCD.

• Double-Fourier engineering of Josephson energy-phase relationships applied to diodes

  A. Mert Bozkurt, Jasper Brookman, Valla Fatemi, Anton R. Akhmerov

  SciPost Phys. 15, 204 (2023) · published 24 November 2023 | Toggle abstract · pdf

  We present a systematic method to design arbitrary energy-phase relations using parallel arms of two series Josephson tunnel junctions each. Our approach employs Fourier engineering in the energy-phase relation of each arm and the position of the arms in real space. We demonstrate our method by engineering the energy-phase relation of a near-ideal superconducting diode, which we find to be robust against the imperfections in the design parameters. Finally, we show the versatility of our approach by designing various other energy-phase relations.

  2 citations

• A functional-analysis derivation of the parquet equation

  Christian J. Eckhardt, Patrick Kappl, Anna Kauch, Karsten Held

  SciPost Phys. 15, 203 (2023) · published 24 November 2023 | Toggle abstract · pdf

  The parquet equation is an exact field-theoretic equation known since the 60s that underlies numerous approximations to solve strongly correlated Fermion systems. Its derivation previously relied on combinatorial arguments classifying all diagrams of the two-particle Green's function in terms of their (ir)reducibility properties. In this work we provide a derivation of the parquet equation solely employing techniques of functional analysis namely functional Legendre transformations and functional derivatives. The advantage of a derivation in terms of a straightforward calculation is twofold: (i) the quantities appearing in the calculation have a clear mathematical definition and interpretation as derivatives of the Luttinger-Ward functional; (ii) analogous calculations to the ones that lead to the parquet equation may be performed for higher-order Green's functions potentially leading to a classification of these in terms of their (ir)reducible components.

• Interpolating between the gauge and Schrödinger pictures of quantum dynamics

  Sayak Guha Roy, Kevin Slagle

  SciPost Phys. Core 6, 081 (2023) · published 24 November 2023 | Toggle abstract · pdf

  Although spatial locality is explicit in the Heisenberg picture of quantum dynamics, spatial locality is not explicit in the Schrödinger picture equations of motion. The gauge picture is a modification of Schrödinger's picture such that locality is explicit in the equations of motion. In order to achieve this explicit locality, the gauge picture utilizes (1) a distinct wavefunction associated with each patch of space, and (2) time-dependent unitary connections to relate the Hilbert spaces associated with nearby patches. In this work, we show that by adding an additional spatially-local term to the gauge picture equations of motion, we can effectively interpolate between the gauge and Schrödinger pictures, such that when this additional term has a large coefficient, all of the gauge picture wavefunctions approach the Schrödginer picture wavefunction (and the connections approach the identity).

• Extensions of realisations for low-dimensional Lie algebras

  Iryna Yehorchenko

  SciPost Phys. Proc. 14, 048 (2023) · published 24 November 2023 | Toggle abstract · pdf

  We find extensions of realisations of some low-dimensional Lie algebras, in particular, for the Poincaré algebra for one space dimension. Using inequivalent extensions, we performed comprehensive classification of relative differential invariants for these Lie algebras. We show difference between classification of extensions of realisations, and classification of nonlinear realisations of Lie algebras.

• On the spin content of the classical massless Rarita-Schwinger system

  Mauricio Valenzuela, Jorge Zanelli

  SciPost Phys. Proc. 14, 047 (2023) · published 24 November 2023 | Toggle abstract · pdf

  We analyze the Rarita-Schwinger massless theory in the Lagrangian and Hamiltonian approaches. At the Lagrangian level, the standard gamma-trace gauge fixing constraint leaves a 1/2 and a 3/2 propagating Poincaré group helicities. At the Hamiltonian level, the result depends on whether the Dirac conjecture is assumed or not. In the affirmative case, a secondary first class constraint is added to the total Hamiltonian and a corresponding gauge fixing condition must be imposed, completely removing the 1/2 sector. In the opposite case, the 1/2 field propagates and the Hamilton field equations match the Euler-Lagrange equations.

  2 citations

• The parastatistics of braided Majorana fermions

  Francesco Toppan

  SciPost Phys. Proc. 14, 046 (2023) · published 24 November 2023 | Toggle abstract · pdf

  This paper presents the parastatistics of braided Majorana fermions obtained in the framework of a graded Hopf algebra endowed with a braided tensor product. The braiding property is encoded in a t-dependent 4×4 braiding matrix $B_t$ related to the Alexander-Conway polynomial. The nonvanishing complex parameter t defines the braided parastatistics. At t=1 ordinary fermions are recovered. The values of t at roots of unity are organized into levels which specify the maximal number of braided Majorana fermions in a multiparticle sector. Generic values of t and the t=-1 root of unity mimick the behaviour of ordinary bosons.

• Construction of matryoshka nested indecomposable N-replications of Kac-modules of quasi-reductive Lie superalgebras, including the sl(m/n) and osp(2/2n) series

  Jean Thierry-Mieg, Peter D. Jarvis, Jerome Germoni, Maria Gorelik

  SciPost Phys. Proc. 14, 045 (2023) · published 24 November 2023 | Toggle abstract · pdf

  We construct a new class of finite dimensional indecomposable representations of simple superalgebras which may explain, in a natural way, the existence of the heavier elementary particles. In type I Lie superalgebras sl(m/n) and osp(2/2n), one of the Dynkin weights labeling the finite dimensional irreducible representations is continuous. Taking the derivative, we show how to construct indecomposable representations recursively embedding N copies of the original irreducible representation, coupled by generalized Cabibbo angles, as observed among the three generations of leptons and quarks of the standard model. The construction is then generalized in the appendix to quasi-reductive Lie superalgebras.

• Towards higher super-$\sigma$-model categories

  Rafał R. Suszek

  SciPost Phys. Proc. 14, 044 (2023) · published 24 November 2023 | Toggle abstract · pdf

  A simplicial framework for the gerbe-theoretic modelling of supercharged-loop dynamics in the presence of worldsheet defects is discussed whose equivariantisation with respect to global supersymmetries of the bulk theory and subsequent orbit decomposition lead to a natural stratification of and cohomological superselection rules for target-space supergeometry, expected to encode essential information on the quantised 2d field theory. A physically relevant example is analysed in considerable detail.

• Segal's contractions, AdS and conformal groups

  Daniel Sternheimer

  SciPost Phys. Proc. 14, 043 (2023) · published 24 November 2023 | Toggle abstract · pdf

  Symmetries and their applications always played an important role in I.E. Segal's work. I shall exemplify this, starting with his correct proof (at the Lie group level) of what physicists call the "O'Raifeartaigh theorem", continuing with his incidental introduction in 1951 of the (1953) Inönü-Wigner contractions, of which the passage from AdS (SO(2,3)) to Poincaré is an important example, and with his interest in conformal groups in the latter part of last century. Since the 60s Flato and I had many fruitful interactions with him around these topics. In a last section I succintly relate these interests in symmetries with several of ours, especially elementary particles symmetries and deformation quantization, and with an ongoing program combining both.