Intro to String Theory: Lightcone Gauge & Oscillators

In summary, the Lightcone gauge is defined as ##X^u=\tau=1/\sqrt{2}(X^0+X^{D-1})## and the mode expansions can be solved for one oscillator in terms of all the others using this relation. The notation ##X^{D-1}## refers to any spatial coordinate perpendicular to the infinite momentum direction, represented by ##X^0##. Each string is made up of harmonic oscillators, with ##n## representing the number of the oscillator in the string. This relation reduces the number of equations to solve by one.
  • #1
binbagsss
1,254
11
Lightcone gauge is ##X^u=\tau=1/\sqrt{2}(X^0+X^{D-1})## (1)

The mode expansions are:
modes.png


My book says 'it is possible to solve for one of the oscillators in terms of all the others' with this relation.

What is a oscillator? Is this any of the ##X^{D}## coordinates, what exactly does ##n## represent, 'frequencies' of a given oscillator?

Does the notation ## X^{D-1}## refer to any spatial coordinate that is the preferred choice?

So basically the relation (1) reduces the number of equations to solve by one, is this what this statement means?
 
Physics news on Phys.org
  • #2
I think X0 is the infinite momentum direction i.e. the direction in which the string is travelling. XD-1 are the dimensions perpendicular to X0, the -1 is to remove the time dimension. Each string comprises a number of mass points which are described as harmonic oscillators, n is the number of the oscillator in the string.
 

1. What is the Lightcone Gauge in String Theory?

The Lightcone Gauge is a mathematical tool used in String Theory to simplify equations and make calculations more manageable. It is a specific set of conditions that restrict the possible solutions to the equations, leading to a more elegant and concise representation of the theory.

2. How does the Lightcone Gauge relate to the concept of lightcones?

The Lightcone Gauge gets its name from the concept of lightcones in physics. In String Theory, lightcones represent the paths that light takes through spacetime. The Lightcone Gauge conditions are based on the properties of these lightcones and are used to reduce the number of dimensions that need to be considered in the equations.

3. What role do oscillators play in String Theory?

Oscillators are fundamental building blocks in String Theory. They represent the vibrational modes of the string and are used to describe the different particles and forces in the theory. The Lightcone Gauge is often applied to the equations involving oscillators to simplify the calculations.

4. How does String Theory incorporate both quantum mechanics and general relativity?

String Theory is a type of quantum theory that attempts to combine the principles of quantum mechanics and general relativity. It does this by replacing the point-like particles of quantum mechanics with tiny, one-dimensional strings. The Lightcone Gauge is one of the mathematical tools used to reconcile these two theories.

5. What are some current challenges in understanding String Theory?

Despite its potential to unify quantum mechanics and general relativity, String Theory is still a developing field with many unanswered questions. Some of the current challenges include understanding the implications of extra dimensions, resolving contradictions between different versions of the theory, and finding experimental evidence to support its predictions.

Similar threads

I Some thoughts about Bell's string paradox alternatives
    • Special and General Relativity
3
Replies
75
Views
3K
A Solve Conditions to Preserve Bondi Gauge Vector Field
    • Special and General Relativity
Replies
1
Views
838
A Can We Construct a Coordinate Chart Where Bell Observers Are At Rest?
    • Special and General Relativity
Replies
11
Views
391
A Basic Scheme and Fundamental Equations of String Theory
    • Beyond the Standard Models
Replies
26
Views
656
I Proper time in a curved space
    • Special and General Relativity
2
Replies
48
Views
3K
A Two Questions about Novikov Coordinates
    • Special and General Relativity
Replies
8
Views
1K
B Looking for help understanding string theory
    • Other Physics Topics
Replies
10
Views
2K
I Is loop quantum gravity dual to CFT?
    • Beyond the Standard Models
Replies
13
Views
1K
I Embeddings of Gauge Group in Einstein-Yang-Mills Theory
    • Special and General Relativity
Replies
1
Views
843
I Understanding Frequency in Rindler Coordinates for a Scalar Massless Field
    • Special and General Relativity
Replies
2
Views
871

Hot Threads

Recent Insights

Back
Top