Some physics notes

 

Negative Energy States in Quantum Theory

Negative Energy States in Quantum Theory

https://arxiv.org/abs/2001.11345

We analyze the Lagrangian density and canonical stress-energy tensor for the Dirac equation, where the Dirac bispinor has been recast as a multivector set of fields. For the massless Dirac field, the sign of the energy density is determined by the relative phase of uncoupled even- and odd-grade field components. These components become coupled in the massive Dirac equation, and the sign of the energy is determined by their spatial parity. The corresponding stress-energy tensors for the second-order equations also admit negative energy states, with the sign of the energy density again dependent on field parity. We apply the same multivector approach to electromagnetism, constructing new Lagrangian and energy densities in which the vector potential and the electromagnetic field are treated as independent field degrees of freedom.

Here's what I've been up to:

On the Physical Interpretation of the Dirac Wavefunction

https://arxiv.org/abs/1707.05198

Using the language of the Geometric Algebra, we recast the massless Dirac bispinor as a set of Lorentz scalar, bivector, and pseudoscalar fields that obey a generalized form of Maxwell's equations of electromagnetism. The spinor's unusual 4-pi rotation symmetry is seen to be a mathematical artifact of the projection of these fields onto an abstract vector space, and not a physical property of the dynamical fields themselves. We also find a deeper understanding of the spin angular momentum and other Dirac field bilinears in terms of these fields and their corresponding analogues in classical electromagnetism.

On the Physical Interpretation of the Dirac Wavefunction II: The Massive Dirac Field

https://arxiv.org/abs/1806.05545

Using the language of the Geometric Algebra, we recast the massive Dirac bispinor as a set of Lorentz scalar, vector, bivector, pseudovector, and pseudoscalar fields that obey a generalized form of Maxwell's equations of electromagnetism. This field-based formulation requires careful distinction between geometric and non-geometric implementations of the imaginary unit scalar in the Dirac algebra. This distinction, which is obscured in conventional treatments, allows us to find alternative constructions of the field bilinears and a more natural interpretation of the discrete C, P, and T transformations.

Faith

Apparently faith can regenerate a destroyed brainstem. News to me.

Ladytron

Embedding is disabled, but this video must be watched:

http://www.youtube.com/watch?v=dtqGoHouoE0

Coco

Excerpt from "A headshaking work of staggering banality"

He is a couple inches over six feet, fairly skinny, looks like a cross between Jemaine Clement and a young Harrison Ford who's been tied up inside a burlap sack, thrown in the trunk of a Cadillac that is then lit on fire and rolled down a mountainside highway and allowed to roll off the shoulder, overturning and bursting into flames, plummeting hundreds of feet before exploding as it crashes onto the ground of the valley below. Imagine that scenario exactly as described, and you will know exactly what he looks like.