John R. Hiller

We solve the Schrödinger-Newton problem of Newtonian gravity coupled to a nonrelativistic scalar particle for solutions with axial symmetry. The gravitational potential is driven by a mass density assumed to be proportional to the probability density of the scalar. Unlike related calculations for condensates of ultralight dark matter or boson stars, no assumption of spherical symmetry is made for the effective gravitational potential. Instead, the potential has only axial symmetry, consistent with the axial symmetry of the particle’s probability density for eigenstates of L z . With total angular momentum no longer a good quantum number, there are, in general, contributions from a range of partial waves. This permits us to study the partial-wave content of self-consistent solutions of the Schrödinger-Newton system.

We compute a nonperturbative effective potential between two static fermions in light-front Yukawa theory as a Hamiltonian eigenvalue problem. Fermion pair production is suppressed, to make possible an exact analytic solution in the form of a coherent state of bosons that form clouds around the sources. The effective potential is essentially an interference term between individual clouds. The model is regulated with Pauli-Villars bosons and fermions, to achieve consistent quantization and renormalization of masses and couplings. This extends earlier work on scalar Yukawa theory where Pauli-Villars regularization did not play a central role. The key result is that the nonperturbative solution restores rotational symmetry even though the light-front formulation of Yukawa theory, with its preferred axis, appears antithetical to such a symmetry. Published by the American Physical Society 2024

We use the Klein-Gordon equation in a curved spacetime to construct the relativistic analog of the Schrödinger-Newton problem, where a scalar particle lives in a gravitational potential well generated by its own probability distribution. A static, spherically symmetric metric is computed from the field equations of general relativity, both directly and as modeled by a perfect-fluid assumption that uses the Tolman-Oppenheimer-Volkov equation for hydrostatic equilibrium of the mass density. The latter is appropriate for a Hartree approximation to the many-body problem of a bosonic star. The simultaneous self-consistent solution of the Klein-Gordon equation in this curved spacetime then yields solitons with a range of radial excitations. We compare results with the nonrelativistic case.

We compute an effective potential between two fixed sources in light-front quantization of a quenched scalar Yukawa theory that models the interaction of complex scalar fields through the exchange of a neutral scalar. Despite the breaking of explicit rotational symmetry by the use of light-front coordinates, the effective potential is rotationally symmetric and matches the standard Yukawa potential for scalar exchange. The neutral scalar field is represented by a coherent state, which is obtained nonperturbatively as an eigenstate of our model Hamiltonian, with the eigenenergy determining the effective potential. The sources are represented by wave packets that are fixed with respect to ordinary time, but move in light-front coordinates. The theory is quenched, to remove pair-production processes that would otherwise cause the spectrum to be unbounded from below. For divergent contributions we consider both a simple momentum cutoff and a Pauli-Villars regularization, with the divergence absorbed by a renormalized mass for the sources.

We explore the convergence of the light-front coupled-cluster (LFCC) method in the context of two-dimensional quenched scalar Yukawa theory. This theory is simple enough for higher-order LFCC calculations to be relatively straightforward. The quenching is to maintain stability; the spectrum of the full theory with pair creation and annihilation is unbounded from below. The basic interaction in the quenched theory is only emission and absorption of a neutral scalar by the complex scalar. The LFCC method builds the eigenstate with one complex scalar and a cloud of neutrals from a valence state that is just the complex scalar and the action of an exponentiated operator that creates neutrals. The lowest order LFCC operator creates one; we add the next order, a term that creates two. At this order there is a direct contribution to the wave function for two neutrals and one complex scalar and additional contributions to all higher Fock wave functions from the exponentiation. Results for the lowest order and this new second-order approximation are compared with those obtained with standard Fock-state expansions. The LFCC approach is found to allow representation of the eigenstate with far fewer functions than the number of wave functions required in a converged Fock-state expansion.