Author Archives: anuj
Schrödinger’s Space-Time Structure – Chapter 1
Let’s work through Erwin Schrödinger’s Space-Time Structure one chapter at a time, explaining both the argument and the mathematics. The book’s overall approach Schrödinger builds spacetime geometry in three stages:…
write this out in expanded form
The repeated index \(\nu\) means sum over all four coordinates, while \(\mu\) labels which transformed coordinate we mean:\ Writing out all four equations:\ dx'^1 &= \frac{\partial x'^1}{\partial x^0}dx^0 +\frac{\partial x'^1}{\partial…
Scalar Lagrangian Full Expansion
For a real scalar field \(\phi(x)\), the standard interacting Lagrangian density is\ Using natural units, \(\hbar=c=1\), and the metric \(\eta_{\mu\nu}=\operatorname{diag}(+1,-1,-1,-1)\), let us expand each part. 1. Expand the spacetime derivatives…
It from Qubit paper by David Deutsch
It from Qubit: David Deutsch on Quantum Information and Reality David Deutsch’s “It from Qubit” (2002) argues that quantum information provides a powerful way to understand physical reality—but cannot, by…
Renormalization in QFT with a few examples
Renormalization is the process of relating the parameters in a quantum field theory to quantities we actually measure. It also explains why the effective strength of an interaction changes with…
Product States – what does it mean to multiply the wavefunctions of two separate particles that are interacting?
A useful distinction is: Product state: We can assign each particle its own wavefunction and multiply them to get the joint amplitude. Entangled state: Only the combined system has a…
Relativistic causality does not require every two-point function to vanish outside the light cone. It requires local observables to commute there = [ϕ(x),ϕ(y)]=0for spacelike separation.
The key distinction is between:correlation\text{correlation} andcausal influence.\text{causal influence}. A two-point function measures correlation. A commutator measures whether one local operation can affect another. 1. The two-point function can be nonzero For…
Feynman’s 1949 paper – Space-Time Approach to Quantum Electrodynamics
Feynman’s Spacetime Approach to QED: Opening Pages Explained These opening two pages are Feynman’s roadmap for a new way of calculating quantum electrodynamics. He is not yet deriving the machinery;…
Peskin and Schroeder’s Problem 2.1 is really about a subtle question…
If Maxwell’s equations follow from a perfectly Lorentz- and gauge-invariant Lagrangian, why does the straightforward Noether energy–momentum tensor look neither symmetric nor gauge invariant? The solution has two stages: derive…
Vacuum energy of particle antiparticle pairs may be responsible for the value of cosmological constant?
In short, No. There is an enormous discrepancy. However, this did not strictly disprove the idea that vacuum energy contributes to the cosmological constant. It showed that the simplest quantum-field-theory…