Related papers: Quantization of the Interacting Non-Hermitian High…

This work addresses the quantization of a self-interacting higher order time derivative theory using path integrals. To quantize this system and avoid the problems of energy not bounded from below and states of negative norm, we observe the…

Higher-order quantum theory is an extension of quantum theory where one introduces transformations whose input and output are transformations, thus generalizing the notion of channels and quantum operations. The generalization then goes…

There exist several good reasons why one may wish to add a total derivative to an interaction in quantum field theory, e.g., in order to improve the perturbative construction. Unlike in classical field theory, adding derivatives in general…

We present a relationship between noncommutativity and higher order time derivative theories using a method perturbative. We introduce a generalization of the Chern-Simons Quantum Mechanics for higher order time derivatives. This model…

Higher Time Derivative Theories are generated by considering space-time rotated KdV and mKdV systems. These systems are then studied to see if/how instabilities, usually associated with higher time derivative theories, manifest on the…

We extend the perturbative approach developed in an earlier work to deal with Lagrangians which have arbitrary higher order time derivative terms for both bosons and fermions. This approach enables us to find an effective Lagrangian with…

Complex networks have become the main paradigm for modelling the dynamics of interacting systems. However, networks are intrinsically limited to describing pairwise interactions, whereas real-world systems are often characterized by…

If a higher derivative theory arises from a transformation of variables that involves time derivatives, a tailor-made Hamiltonian formulation is shown to exist. The details and advantages of this elegant Hamiltonian formulation, which…

Higher-order interactions provide a nuanced understanding of the relational structure of complex systems beyond traditional pairwise interactions. However, higher-order network analyses also incur more cumbersome interpretations and greater…

The effect of inclusion of higher-order interactions in the {\it XY} model on critical properties is studied by Monte Carlo simulations. It is found that an increasing number of the higher-order terms in the Hamiltonian modifies the shape…

In the context of non-relativistic quantum field theory, a method is proposed for multiplying field operators at the same spatial point and obtaining regular (i.e. rigorously defined) interaction terms for the Hamiltonian. The basic idea is…

Canonical analysis leading to formal quantisation of the higher derivative theories are considered. The first order formalism is adopted where all the configuration space variables along with their higher time derivatives are considered to…

We consider the canonical quantization of a generalized two-dimensional massive fermion theory containing higher odd-order derivatives. The requirements of Lorentz invariance, hermiticity of the Hamiltonian and absence of tachyon…

The concept of effective particles as degrees of freedom in a relativistic quantum field theory is defined using a non-perturbative renormalization group procedure for Hamiltonians. However, every candidate for a basic physical theory…

In this work we analyze systems described by Lagrangians with higher order derivatives in the context of the Hamilton-Jacobi formalism for first order actions. Two different approaches are studied here: the first one is analogous to the…

In many complex systems, elements interact via time-varying network topologies. Recent research shows that temporal correlations in the chronological ordering of interactions crucially influence network properties and dynamical processes.…

We discuss the extent to which it is necessary to include higher-derivative operators in the effective field theory of general scalar-tensor theories. We explore the circumstances under which it is correct to restrict to second-order…

We review a perturbative approach to deal with Lagrangians with higher or infinite order time derivatives. It enables us to construct a consistent Poisson structure and Hamiltonian with only first time derivatives order by order in…

Many complex systems often contain interactions between more than two nodes, known as higher-order interactions, which can change the structure of these systems in significant ways. Researchers often assume that all interactions paint a…

First-order automatic differentiation is a ubiquitous tool across statistics, machine learning, and computer science. Higher-order implementations of automatic differentiation, however, have yet to realize the same utility. In this paper I…