The process algebra has been used successfully to provide a novel formulation of quantum mechanics in which non-relativistic quantum mechanics (NRQM) emerges as an effective theory asymptotically. The process algebra is applied here to the formulation of quantum field theory. The resulting QFT is intuitive, free from divergences and eliminates the distinction between particle, field and wave. There is a finite, discrete emergent space-time on which arise emergent entities which transfer information like discrete waves and interact with measurement processes like particles. The need for second quantization is eliminated and the particle and field theories rest on a common foundation, clarifying and simplifying the relationship between the two.The process algebra has been used successfully to provide a novel formulation of quantum mechanics in which non-relativistic quantum mechanics (NRQM) emerges as an effective theory asymptotically. The process algebra is applied here to the formulation of quantum field theory. The resulting QFT is intuitive, free from divergences and eliminates the distinction between particle, field and wave. There is a finite, discrete emergent space-time on which arise emergent entities which transfer information like discrete waves and interact with measurement processes like particles. The need for second quantization is eliminated and the particle and field theories rest on a common foundation, clarifying and simplifying the relationship between the two.

arXiv:1502.02346Feb 9, 20150 citations

Quantum Field Theory

CHRISTOF WETTERICH

Fundamental theories of physicsJan 1, 20250 citations

Multi-time Quantum Field Theory

Matthias Lienert, Sören Petrat, Roderich Tumulka

SpringerBriefs in physicsJan 1, 20200 citations

Discretizing quantum field theories for quantum simulation

Terry Farrelly, Julien Streich

To date, all proposed quantum algorithms for simulating quantum field theory (QFT) simulate (continuous-time) Hamiltonian lattice QFT as a stepping stone. Two overlooked issues are how large we can take the timestep in these simulations while getting the right physics and whether we can go beyond the standard recipe that relies on Hamiltonian lattice QFT. The first issue is crucial in practice for, e.g., trapped-ion experiments which actually have a lower bound on the possible ratio of timestep to lattice spacing. To this end, we show that a timestep equal to or going to zero faster than the spatial lattice spacing is necessary for quantum simulations of QFT, but far more importantly a timestep equal to the lattice spacing is actually sufficient. To do this, first for $ϕ^4$ theory, we give a quantum circuit exactly equivalent to the real-time path integral from the discrete-time Lagrangian formulation of lattice QFT. Next we give another circuit with no lattice QFT analogue, but, by using Feynman rules applied to the circuit, we see that it also reproduces the correct continuum behaviour. Finally, we look at non-abelian gauge fields, showing that the discrete-time lattice QFT path-integral is exactly equivalent to a finite-depth local circuit. All of these circuits have an analogue of a lightcone on the lattice and therefore are examples of quantum cellular automata. Aside from the potential practical benefit of these circuits, this all suggests that the path-integral approach to lattice QFT need not be overlooked in quantum simulations of physics and has a simple quantum information interpretation.To date, all proposed quantum algorithms for simulating quantum field theory (QFT) simulate (continuous-time) Hamiltonian lattice QFT as a stepping stone. Two overlooked issues are how large we can take the timestep in these simulations while getting the right physics and whether we can go beyond the standard recipe that relies on Hamiltonian lattice QFT. The first issue is crucial in practice for, e.g., trapped-ion experiments which actually have a lower bound on the possible ratio of timestep to lattice spacing. To this end, we show that a timestep equal to or going to zero faster than the spatial lattice spacing is necessary for quantum simulations of QFT, but far more importantly a timestep equal to the lattice spacing is actually sufficient. To do this, first for $ϕ^4$ theory, we give a quantum circuit exactly equivalent to the real-time path integral from the discrete-time Lagrangian formulation of lattice QFT. Next we give another circuit with no lattice QFT analogue, but, by using Feynman rules applied to the circuit, we see that it also reproduces the correct continuum behaviour. Finally, we look at non-abelian gauge fields, showing that the discrete-time lattice QFT path-integral is exactly equivalent to a finite-depth local circuit. All of these circuits have an analogue of a lightcone on the lattice and therefore are examples of quantum cellular automata. Aside from the potential practical benefit of these circuits, this all suggests that the path-integral approach to lattice QFT need not be overlooked in quantum simulations of physics and has a simple quantum information interpretation.

arXiv:2002.02643Feb 7, 202010 citations

Quantum Field Theory

Armin Uhlmann

Zeitschrift für Physikalische ChemieJan 1, 19960 citations

ϕ^4

theory, we give a quantum circuit exactly equivalent to the real-time path integral from the discrete-time Lagrangian formulation of lattice QFT. Next we give another circuit with no lattice QFT analogue, but, by using Feynman rules applied to the circuit, we see that it also reproduces the correct continuum behaviour. Finally, we look at non-abelian gauge fields, showing that the discrete-time lattice QFT path-integral is exactly equivalent to a finite-depth local circuit. All of these circuits have an analogue of a lightcone on the lattice and therefore are examples of quantum cellular automata. Aside from the potential practical benefit of these circuits, this all suggests that the path-integral approach to lattice QFT need not be overlooked in quantum simulations of physics and has a simple quantum information interpretation.