Explain Field Theory in Detail - No Quotes Needed

[Stu21]

If some one could please explain what a field is in as much detail as possible please. don't be shy I love a challenge.

My understanding is that a field is a precise area surrounding its source. depending on the field you get different effects. For example with the higgs field, the higgs boson is the particle responsible for the field and the field gives other particles mass. this field also permeates the universe, is that because of many of these particles scattered everywhere throughout the universe or because the field they emit is very large. now i know that the photon is the EM force carrier, but i don't understand how an electrical field works, because to my understanding electricity makes use of electrons. can someone explain this please.

 

[Simon Bridge]

Field theory is a very abstract bit of math.

The "field" of Field Theory describes the math, not the Universe.
Probably your best bet is to read around the topic and then ask questions where you get stuck. eg. http://en.wikipedia.org/wiki/Field_(physics ) ... but don't stop there.

In the standard model, electromagnetic fields are mediated by photons. Charges act as sources of the field. In this model, the Higgs boson is thought of as a ripple in the Higgs field. (since you mentioned it.) But you seriously need to walk before you run with this one.

Basically you get a feel for how fields behave by doing a lot of math. Enjoy.

 

[Drakkith]

now i know that the photon is the EM force carrier, but i don't understand how an electrical field works, because to my understanding electricity makes use of electrons. can someone explain this please.

Electricity, which isn't a very good term in the first place, just has to do with the movement of charges through circuits. Electromagnetism is the actual fundamental force that deals with electricity and magnetism along with light. I highly recommend you learn the basics of electromagnetism and other classical theories before attempting to learn about Field Theories.

 

[dipstik]

old school field theory is about lines of force extending from one object, affecting another object. the way these extentions work is by the potential energy of the ensemble, so the electric, magnetic or gravitational forces about one body modulates the force on another body due to position, charge, mass etc.

there are newer field theories, like general relativity and quantum field theory.

GR talks about spacetime being modulated by energy/mass
QFT talks about particles being excitations of a field with some particular mechanics (from the lagrangian density), and will spit out probabilities of certin events occurring.

 

[cosmik debris]

There is probably quite a difference between the idea of a field in Maths and Physics although of course one depends on the other. The mathematical idea of a field was used in physics to explain the interaction of objects at a distance from one another. The idea is that a field has values at any co-ordinate that can be calculated from a point nearby. By moving through this field you can calculate the effect on each point in turn until you have connected the two objects. This provide a mechanism for "action at a distance".

 

[Simon Bridge]

iirc: that math idea of a field is a superset of the physics idea - that's usually how it works out. That's not a bad description of the motivation for field theory though - the idea is that you don't need to know anything about what "causes" the force in order to experience the force.

We have a bunch of answers now with different, but related, slants. Time to hear from stu again to find out where to put the emphasis :)

 

[Studiot]

Time to hear from stu again to find out where to put the emphasis :)

Good point.

A field is a region of space that may include all or part of space where we can assign a particular and unique value to some property of interest at every point.

This value may be a scalar, in which case we have a Scalar Field
Such a field might be the temperatures at all points within a metal bar that has one end in ice and the other in boiling water.

We can draw contours or equithermal lines or isotherms connecting points of equal temperature.
We can also draw thermal gradient lines perpendicular to these.

Or the field property may be a vector quantity. This is often visualised as assigning a little arrow to every point, showing the magnitude and direction of the vector.

Such a field might be a velocity field in a flowing river. All the arrows would form flowlines in the water and run around in circles where there are eddies.

 

[Stu21]

what I've so far what managed to gather is; that a classic field is a way of describing "action at a distance". A quantum field makes use of quantum particles to help explain the distance part, thus making things even more complicated.

4 main types of fields, scalar, vector, spinor and tensor

Scalar: the relation between the field and a point within the field, coordinate-invariant
Vector: deals with the motion, momentum, magnitude, and other such related attributes of a field..?
spinor: I am not sure.. possibly something to do with the spin of a particle??
Tensor: combines scalars and vectors into one mathematical formula... something like before tensors were developed EM was described using two wave functions, but tensors are able to unify them??

Going back to energy then. current (?in case of electricity the electron?) flows because of reduced voltage at one end causing a flow of electrons from the high voltage end to the low voltage end. this is the electro part of EM. this flow of electrons in turn produces a negative field around the wire. if say a positive field were introduced and they were both manipulated properly then one could produce electricity, this is also know as electromgnatism

Am i catching any of this?

 

[Mark M]

A scalar field is a field that takes a single value at every point, and nothing else. It has one degree of freedom. An example if the Higgs field, which takes only a vacuum expectation value. Particles that compose a scalar field are naturally called scalar bosons. A vector field has not only a value at every point, but an associated direction. The electric field, the magnetic field and Newton's gravitational field are all examples of vector fields. They are relevant to forces that occur over distance, whereas scalar fields are concerned only with one point at a time. We can represent a vector field with a vector at every point in the field.

A tensor field has a tensor at every point, rather than a vector. Tensors are like vectors, except they have more than one basis for each orthogonal axis. For a vector, we can specify a unit vector in the x, y and z directions to form a basis from which we can build any vector we like. Since they require
only one basis to be summed over, vectors are tensors of rank one. Higher rank tensors have more than one basis vector for each component. An example is the the gravitational field in general relativity, which is the curvature of space-time. This is represented by the Riemann curvature tensor. The electromagnetic field is also a tensor field, as it has both an electric and magnetic vector at every point.

A spinor field represents an object that is a spinor. A spinor is a mathematical object that must be rotated more than once to be brought back to it's original value. An example of this is the wavefunction of a particle. So, the field associated with any particle in quantum field theory is a spinor field (fermions are a two-component spinor). Note that 'rotation' is not the normal rotation in space O(3), but is a linear operator. To bring a fermion back to it's original state you must rotate it's wavefunction twice through the complex plane.

 

[Studiot]

Are you sure this is not too restrictive?