Multiple Dimensions in Quantum Theories

[lch7]

Will someone please explain to me how a theory, such as a quantum field theory, be expressed in more than three dimensions? Is this referring to the spatial dimensions we live in now, or what? And how does someone even begin to ponder these multiple dimensions?

 

[ModusPwnd]

And how does someone even begin to ponder these multiple dimensions?

By doing the math. You mention quantum field theory, have you not been through "regular" quantum mechanics? Hilbert space is infinite dimensional. Or how about phase space in stat. mech. Its got a lot of dimensions, a lot. These are not 'physical spaces', but they are spaces with many dimensions. If you haven't studied any of this, check out the wikipedia:http://en.wikipedia.org/wiki/Dimension_(mathematics_and_physics)
" the dimension of a space or object is informally defined as the minimum number of coordinates needed to specify any point within it."I don't know any quantum field theory. Some expert will chime in and kick some knowledge I'm sure. I don't think there is higher spatial dimensions in qft... I think that is a part of hypotheticals like string theory, etc.

 

[The_Duck]

Mathematically, it's very easy to formulate any sort of theory, quantum mechanical or otherwise, in any number of dimensions. Instead of dealing with points labeled by three coordinates, (x, y, z), just start talking about points labeled by, say, 5 coordinates, (x, y, z, v, w). Now you're doing physics in five spatial dimensions.

Visualizing it is another matter. Some advice I once heard: to visualize, say, 9-dimensional space, first visualize N-dimensional space and then let N go to 9.

 

[ModusPwnd]

This is the classic book on the matter (of visualizing dimensions). Its a fun, quick read.

http://en.wikipedia.org/wiki/Flatland

 

[lch7]

Thank you all! Very interesting.