Related papers: A Simple Introduction to Particle Physics Part II
This is an overview of higher structural constructions in physics. The main motivations of our current attempt are as follows: (i) to provide a brief introduction to derived algebraic geometry, (ii) to understand how derived objects…
We propose a geometric setting of the axiomatic mathematical formalism of quantum theory. Guided by the idea that understanding the mathematical structures of these axioms is of similar importance as was historically the process of…
This is lecture notes for a course given at the PCMI Summer School "Quantum Field Theory and Manifold Invariants" (July 1 -- July 5, 2019). I describe basics of gauge-theoretic approach to construction of invariants of manifolds. The main…
As a community, our goal is to understand the fundamental nature of energy, matter, space, and time, and to apply that knowledge to understand the birth, evolution and fate of the universe. Our scope is broad and we use many tools:…
Particle physics has evolved a coherent model that characterizes forces and particles at the most elementary level. This Standard Model, built from many theoretical and experimental studies, is in excellent accord with almost all current…
These notes have been prepared as reading material for the mini-course given by the author at the "2019 Graduate Summer School" at Park City Mathematics Institute - Institute for Advanced Study. We begin by introducing Higgs bundles and…
In these lectures, I discuss the role of symmetries in particle physics. I begin by discussing global symmetries and show that they can be realized differently in nature, depending on whether or not the vacuum state is left invariant by the…
I discuss some central issues in particle physics which are potentially relevant to cosmology. I first briefly review the present (glorious) experimental status of the Standard Model, emphasizing that it provides a firm foundation both for…
The question that guides our discussion is how did the geometry and particles come into being. The present theory reveals primordial deeper structures underlying fundamental concepts of contemporary physics. We begin with a drastic revision…
After a very brief review of twentieth century elementary particle physics, prospects for the next century are discussed. First and most important are technological limits of opportunities; next, the future experimental program, and finally…
As in the case of the other gauge field theories, there is so called ``gauge'' also in general relativity. This ``gauge'' is unphysical degree of freedom. There are two kinds of ``gauges'' in general relativity. These are called the first-…
In this work we explore the geometrical interpretation of gauge theories through the formalism of fiber bundles. Moreover, we conduct an investigation in the topology of fiber bundles, providing a proof of the Classification Theorem. In the…
The goal of these lectures is to introduce readers with a basic knowledge of undergraduate physics (specifically non-relativistic quantum mechanics, special relativity, and electromagnetism) to the `current theory of everything': the…
An extremely simple and unified base for physics comes out by starting all over from a single postulate on the common nature of matter and stationary forms of radiation quanta. Basic relativistic, gravitational (G) and quantum mechanical…
To develop an increase in societal interest in the fundamental sciences of particle physics and particularly for maintaining the support structures needed to succeed in experiments that take several decades to develop and complete, requires…
A fibre bundle viewpoint of gauge field theories is reviewed with focus on a possible quantum interpretation. The fundamental quantum properties of non-separability of state spaces is considered in the context of defining the connection on…
Till now, the foundation of quantum physics is still mysterious. To explore the mysteries in the foundation of quantum physics, people always take it for granted that quantum processes must be some types of fields/objects on a rigid space.…
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…
We give a brief overview how to couple general relativity to the Standard Model of elementary particles, within the higher gauge theory framework, suitable for the spinfoam quantization procedure. We begin by providing a short review of all…
We review particle physics model building in type IIB string theory and F-theory. This is a region in the landscape where in principle many of the key ingredients required for a realistic model of particle physics can be combined…