Notes on string theory #6: Enter into the light-cone

Now that we've studied the $latex {S_{NG}}&fg=000000$ and $latex {S_{P}}&fg=000000$ forms of bosonic string action, we turn our attention to the fact that the string will fluctuate. In the next sections of Polchinski's textbook (1.3-1.4), we will study the spectrum of open string fluctuations before moving to the case of closed strings. In doing so, …

Notes on string theory #5: Modifying the Polyakov action (cosmological constant and Ricci scalar)

We come to the conclusion of Section 1.2 in Polchinski's textbook. In this note we'll discuss how there are two possible modifications that we can make to the Polyakov action (see last note) that preserve Poincaré invariance. The first is a cosmological constant term on the worldsheet. The second modification involves the scalar curvature $latex …

Notes on string theory #4: Polyakov action

In our ongoing read through of Polchinski's textbook, we left off on page 12 having studied the first principle Nambu-Goto action $latex {S_{NG}}&fg=000000$ for the string. We have glimpsed early on why string theory is a generalisation - or, one could also say, deformation - of point particle theory. The generalisation from point particles to …

Notes on string theory #3: Nambu-Goto action

1. Introduction I haven't been keeping up with this as much as I would like, mainly because I have been busy. But I am committed to continuing to reupload many of my notes on Polchinski's textbooks. It is fun for me to go through it all again in my spare time, and I've noticed that …

Notes on string theory #2: The relativistic point particle

1. Introduction In Chapter 1 of Polchinski's textbook, we start with a discussion on the relativistic point particle (pp. 9-11). String theory proposes that elementary particles are not pointlike, but rather 1-dimensional extended objects (i.e., strings). In fact, string theory (both the bosonic string in Volume 1 of Polchinski and the superstring that comprises much …

Notes on string theory #1: The non-relativistic string

The study of waves has far reaching applications throughout physics (and across the sciences). Fundamental physics is no exception. Essential for understanding waves is understanding oscillation, and as one will recall from classical mechanics a concept of fundamental importance in this regard is the harmonic oscillator. A simple harmonic oscillator can then also be generalised …

Reading Polchinski – My notes on string theory

When I was in the first year of my undergraduate degree, I started self-studying string theory. At that time, I set myself the task of working through Joe Polchinski's two volume textbook, String Theory. It was honestly one of the best years of my life, despite the general uncertainty about my academic future at the …