相关论文: Three Easy Pieces (in tribute to Roman Jackiw)

This text offers reminiscences of my personal interactions with Roman Jackiw as a way of looking back at the very fertile period in theoretical physics in the last quarter of the 20th century.

This essay is a tribute to Professor Roman Jackiw on the occasion of his eightieth year. It discusses some ideas about Fermion zero modes and fractional charges and quantum entanglement.

To celebrate Roman Jackiw's 80th birthday, herewith some comments on gravity and gauge theory models in D=3, the chief focus of many of our joint efforts.

Assuming a minimum value for area measurement, the emergence of quantum mechanics can be easily motivated from naive consideration of gravitational force. Here we provide some pedagogical examples and extensions. At the same time, the role…

In this talk I review some of the recent developments in the field of random surfaces and the Dynamical Triangulation approach to simplicial quantum gravity. In two dimensions I focus on the c=1 barrier and the fractal dimension of…

A classical dynamical system in a four-dimensional Euclidean space with universal time is considered. The space is hypothesized to be originally occupied by a uniform substance, pictured as a liquid, which at some time became supercooled.…

On the base of years of experience of working on the problem of the physical foundation of quantum mechanics the author offers principles of solving it. Under certain pressure of mathematical formalism there has raised a hypothesis of…

Our understanding of the four basic concepts of Physics -- space, time, matter and force -- has undergone radical change in the course of work on unification, starting with Maxwell's unification of electricity with magnetism, all the way to…

The logical line is traced of formulation of theory of mechanics founded on the basic correlations of mathematics of hypercomplex numbers and associated geometric images. Namely, it is shown that the physical equations of quantum, classical…

In 1834-1835, Hamilton published two papers that revolutionized classical mechanics. In these papers, he introduced the Hamilton-Jacobi equation, Hamilton's equations of motion and the principle of least action. These three formulations of…

We sketch some connecting relations involving fractional and quantum calculi, fractal structure, thermodynamics, and quantum mechanics.

I recount my personal experience interacting with Roman Jackiw in the 1980s, when we both worked on Chern-Simons theories in three dimensions.

Jackiw and Rebbi found two types of intrinsically stable or `fundamental' soliton (kinks in 1+1 D and magnetic monopoles in 3+1 D) which can carry pieces of elementary-particle charges. After two decades there are no more, and it is argued…

Much progress has been made in the last few decades in developing the necessary mathematics for understanding the full implications of the quantum-mechanical many-body problem and why the material world appears to be as stable as it is…

I review why and how physical states with fractional quantum numbers can occur, emphasizing basic mechanisms in simple contexts. The general mechanism of charge fractionalization is the passage from states created by local action of fields…

Fractional calculus is a couple of centuries old, but its development has been less embraced and it was only within the last century that a program of applications for physics started. Regarding quantum physics, it has been only in the…

The formulation of a complete theory of classical electromagnetism by Maxwell is one of the milestones of science. The capacity of many-body systems to provide emergent mini-universes with vacua quite distinct from the one we inhabit was…

Quantum theory is extremely successful in explaining most physical phenomena, and is not contradicted by any experiment. Yet, the theory has many puzzling features : the occurrence of probabilities, the unclear distinction between the…

Numerical relativity has made big strides over the last decade. A number of problems that have plagued the field for years have now been mostly solved. This progress has transformed numerical relativity into a powerful tool to explore…

We start by presenting a brief summary of fractional quantum mechanics, as means to convey a motivation towards fractional quantum cosmology. Subsequently, such application is made concrete with the assistance of a case study. Specifically,…