What is a photon? I'm trying to get a definitive and clear answer to the question of what a photon actually is.
Textbooks seem to give quite vague explanations, all starting with Einstein's idea that a quanta is a form of light which has a frequency associated with it, finite energy, and is localised in space. The frequency is said to be that of electromagnetic waves. Does it only have a single frequency, or can it have a group? Is the frequency that of the electric field, or the magnetic field, or both, or is it not possible to say? Is it always localised in space, or does it actually disperse, or is either option valid? Can we write down a wavefunction for a photon, or give a set of conditions that wavefunctions must satisfy in order to be considered a photon?
Photons seem to be one of the foundation ideas of quantum mechanics, so I am concerned that without a clear definition or set of concrete examples, the basis for understanding quantum experiments is a little fuzzy.
Remember I'm looking for a clear definition! On the other hand if you think there is no clear definition, I would also like to know.
EDIT: Although this question is assumed to be the same as asking "what is a quantum of light?", according to Lamb's Anti-Photon paper:
"G.N.Lewis, in 1926, coined the word 'photon' to describe something completely different from the Einstein light quantum."
 A: I've seen and studied much on the quantum of electromagnetic energy, which we call photon.  There are a lot of contradictory statements concerning interpretation, but there isn't much debate about the theory.   My conclusion is that it is not a particle like a small bit of something, and it is not a wave as in the oscillations of a medium, and it is not some kind of wave/particle hybrid.   My current thinking is that it is something that is well outside of our ability to understand.  Our brains evolved interpreting ordinary, macroscopic day-to-day objects and phenomena.   The photon (and every other fundamental "particle") is well outside of day-to-day experience.   I think it's some kind of entity that our brain just cannot comprehend.
The picture that I carry around is like this:   electromagnetic fields are constrained by their environment ... free space, cavity, whatever.   The field fills all of the space in question.  Excitations of the field occur at particular locations, such as at a particular atom.  The interactions are localized and the excitations are quantized, so it appears as if a particle has been created.   This picture is working for me, so far, but it undoubtedly has holes.
A: At the present time in physics, the photon is an elementary particle, a member of the table of elementary particles that are the basis for the standard model of physics.


Elementary particles included in the Standard Model

It has zero mass, zero charge and spin one, and it is the gauge boson of the electromagnetic interactions.  In all electromagnetic interactions a photon is involved, either on shell ( mass zero) or virtual within a Feynman diagram.
There exists a quantum mechanical equation which gives a wave function for the photon. It  is a form of  Maxwell's equation the differentials treated  as operators for example here.
The classical electromagnetic fields emerge from a huge accumulation of photons that have through E=h*nu the connection with the frequency of the electromagnetic wave. It is not simple mathematics, but it can be demonstrated. . This article in wikipedia might help in this.
As a general rule, when one is talking of electric and magnetic fields the classical theory is adequate to describe the data. It is only at the level of elementary particles that the photon framework is needed, and there it is quite well defined.
A: "The frequency is said to be that of electromagnetic waves. Does it only have a single frequency, or can it have a group?"
An individual photon can only have one frequency - but it can be any frequency - like, if you take a test, you can only get one score, but it can be any score from 0 to 100.    2 photons can travel in the same direction  close to each other and you can get a mix of colors that way, but a single photon can only have a single frequency and if it's visible light, a single color.
"Is the frequency that of the electric field, or the magnetic field, or both, or is it not possible to say?"
I think, both.
An Electric Field looks like this:

A magnetic field, like this:

Where as a model for a photon has both an Electric field and a magnetic field - at 90 degree angles to each other, and a direction and a wavelength, like so:

Now, I don't know if that's actually what's going on or if that's a simple diagram of convenience.
"Is it always localised in space, or does it actually disperse, or is either option valid?"
I don't think anything in the quantum world is entirely localized in space, but beyond the uncertainty principal, I'm not sure how to answer that. 
I found this on a similar subject with some good answers.    I think the first thing to read up on when trying to understand light, if you haven't already done that, is the wave-particle duality - which is counter-intuitive, but lots of quantum mechanics is counter-intuitive.   I also found this conversation on a similar question with some good answers:
What exactly is a quantum of light?
In short, I think, Knowing what standard model particles are is hard.   We can know how they behave.   I'm not sure we can know what they are.  
and, if any of that is wrong, I invite correction.
