Session G13: Developments in Quantum Field Theory

Live

Quantum simulation of quantum field theories offers a new way to investigate properties of the fundamental constituents of matter. We develop quantum simulation algorithms based on the light-front formulation of relativistic field theories. We analyze a simple theory in 1$+$1D and show how to compute the analogues of parton distribution functions of composite particles in this theory. Upon quantizing the system in light-cone coordinates, the Hamiltonian becomes block diagonal, each block approximating the Fock space with a certain harmonic resolution K. The lower bound on the number of qubits required is O($\surd $K), and we give a complete description of the algorithm in a mapping that requires O($\surd $K logK) qubits and O(K$^{\mathrm{6}}$ ) gates. In higher dimensions, the scaling of the number of qubits remains the same, up to logarithmic factors. This is a notable advantage of the light-front formulation.   

Live

It is not unusual to find divergent solutions after applying the standard methods of perturbation theory to calculate truncated corrections to any set of equations of motion modified perturbatively. In this talk, we show a novel procedure, which not only avoids those divergences; but also improves the accuracy of first-order solutions. Our technique maps the perturbed solution to the renormalization group generators to transform the constant model parameters into time-dependent expressions. Such new model parameters boost the accuracy of the renormalized solutions. Prospectively, this procedure can be extended to the computation of corrected GW waveforms by extra degrees of freedom in modified theories of gravity.   

Live

In this talk, I will present a family of generalization of some well-known theories such as the Pontryagin model, the Husain-Kuchar model, or different formulations of 3-dimensional GR with cosmological constant. When boundaries are included, this family presents an interesting holographic principle: we could obtain relevant theories in both the bulk and the boundary [1]. I will address the interplay between them within the Hamiltonian framework. I will also explain the appearance of some sectors of the phase space in which the dynamics are different. Generalizations of the Pontryagin and Husain-Kuchar actions to manifolds with boundary J. Fernando Barbero G., Bogar Díaz, Juan Margalef-Bentabol, Eduardo J.S. Villaseñor Journal of High Energy Physics 10 (2019) 121 [arXiv:1906.09820]   

Live

Primordial perturbations are responsible for CMB anisotropies and structure formation in the Universe. We believe that the perturbations have their origins in quantum theory, though these effects are hard to detect. I will discuss the quantum dynamics of observable perturbation modes in the presence of interactions during inflation. In particular, I will describe an open quantum system framework that demonstrates a non-Hamiltonian and non-Markovian evolution of observable modes. I will also discuss preliminary results on evolution under a simplifying Markovian approximation and the resulting Green’s functions.   

Live

The time-dependent electromagnetically self-coupled Dirac equation is solved numerically by means of the staggered-leap-frog algorithm. The stability region of the method versus the interaction strength and the ratio of the spatial-grid size over the time-step is established. The expectation values of several dynamic operators are evaluated as functions of time. These include the fermion and electromagnetic energies and the fermion dynamic mass. There is a characteristic time-dependence leading to asymptotic constants of these expectation values. In the case of the fermion mass and charge this amounts to renormalization. The dependence of the expectation values on the spatial-grid size is evaluated and yields finite results due to the finiteness and continuity of the spinor. The contribution of positive and negative energy states to the asymptotic values and the gauge fields is analyzed. A statistical method, employing a canonical ensemble whose temperature is the inverse of the spatial-grid size, is used to remove the momentum-dependence. A result for each spatial-grid size value is obtained. The continuum limit is taken to calculate both the fermion mass and charge. The renormalization mass correction is 10\% and the charge correction is about 30\%.   

Not Participating

Inspired by the simple Hypergeometric resummation algorithm in PRL. 115, 143001 (2015), we developed the Hypergeometric-Meijer G Resummation algorithm that can incorporate all weak-coupling, strong-coupling and Large-order data. We shall shed light on its simplicity and power to predict precise results in different problems in physics from PT-symmetric models, quantomechanical problems as well as critical exponents of the O(N)-symmetric quantum field model. We also stress how within this algorithm one can link exact critical exponents to known parameters from a Large-order parameter, a vey important realization ( for the first time) as explained in our article in \underline {arXiv:1911.03571}.   

Not Participating

We investigate the friction acting on a charged particle moving parallel to an imperfect conductor slab described with the Drude model. In nonrelativistic and ultrarelativistic regimes, the properties of frictions due to the TE and TM modes are quite different. The velocity dependence of the friction is non-monotonic. The friction may be nonzero in the low-resistivity limit when the particle is moving with a high velocity. Other properties of the friction are also studied