Category Archives: Physics

Probability Densities in Quantum Theory

Suppose a particle travelled one dimensionally. Classically, the particle’s behavior should be in line with Newton’s laws of motion. Quantum mechanically, however, one cannot determine the exact position and momentum of the particle and as such is reduced to using a probabilistic interpretation. Here we will explore the notion of a probability density and how one could derive such an artifact from a simple Taylor expansion argument. Continue reading Probability Densities in Quantum Theory

Why Massive Particles are Slow and Lazy

Here we’re going to discuss the equations of motion for a charged particle in a curved spacetime with an electromagnetic tensor, $F_{ab}$, show why massive particles have a contracted $4-$velocity, $u^a$, that is constant along a charged-particle path, and why massive particles move slower than the speed of light.

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Feynman Rules for Ordinary Integrals

Path integral quantum field theory, perhaps single handedly constructed by Richard Feynman, remains both elusive to undergraduates that wish to study the subject and immensely useful for performing the calculations found in quantum field theory due to the path integral formulation being manifestly symmetric between space and time. Here, we will enter the world of path integral quantum field theory by meticulously performing the calculations so that it is accessible to an advanced undergraduate.

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Tensorial Propagators (Part III)

In Part I, we discovered that tensorial propagators in quantum field theory are often non-invertible which poses an issue when one is trying to determine the form of the propagator. Then, in Part II, we discussed possible techniques involving both symmetries and invariants of the Lagrangian. Here, we aim to reveal how invariant quantities may be useful for propagators, and gauge fields specifically, and we will ultimately derive the form of the photon propagator.

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Tensorial Propagators (Part II)

In Part I, we found the central issue when dealing with tensorial propagators $latex -$ they are usually non-invertible. So then how do physicists obtain these propagators? In order to obtain these propagators, they usually exploit gauge invariance. Here, we will discuss what gauge invariance is and continue with our analysis of the photon propagator.

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Path Integral Free Propagator

In quantum field theory, the propagator gives a probability amplitude for a particle traveling from some point $latex (t_i,x_i)$ to $latex (t_f,x_f)$ with a certain energy and momentum. These propagators are the first steps into quantum field theory, I aim to bring these to the masses. The one that is most interesting and easy to grasp is the free propagator for a free field theory. The following derivation is inspired by Anthony Zee’s Quantum Field Theory in a Nutshell of UC Santa Barbara.

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