A question on particles and fields after learning that all particles are actually excitements in their respective field; for analogy: electrons and the electric field, Higgs Bosons and Higgs field; I had this absurd question in my mind, if we were to represent these fields in 2 dimensions and their respective excitements in 3 dimensions ( all of the dimensions mentioned in this question are physical dimensions thus excluding the time dimension ), it would look like this:

(the image above is inaccurate, but aids this topic’s comprehension)
then, if we were to demonstrate the concept in our euclidean world and consider 3 dimensional fields then would we get 4 dimensional waves and excitements?
if so, how come we don’t see these particles’ 4th dimensional attributes and properties? and if we do, what are they?
TL;DR: are excitements in our world’s fields, 4 dimensional (physical dimensions)?
 A: Consider a sound wave moving through the air. This is a wave moving in three dimensions because the pressure at any point in the wave $P(x,y,z)$ is a function of the position $(x,y,z)$. But that doesn't mean sound waves are four dimensional. The thing that varies with position is a pressure not a displacement into a fourth dimension. In your picture, if this were a sound wave the $z$ axis would be pressure not displacement.
The same applies to particle wavefunctions, though we have to be careful here as it is unclear to what extent the wavefunction represents anything physical. This is even more so in QFT since the quantum field we do calculations with is a mathematical object called an operator field. While many of us believe this mathematical object does represent some physical object this belief is far from universal.
A: 
all particles are actually excitements in their respective field; for analogy: electrons and the electric field, Higgs Bosons and Higgs field;

This is the Quantum Field Theory used in the standard model of particle physics. QFTs are used in many quantum mechanical  models . They are based on creation and annihilation operators that create and annihilate particles acting on their quantum mechanical fields.  What you are describing is the way it is used in the Feynman diagrams that calculate crossections and decays, and...
It does not mean that it is a good model to describe a free electron after the interaction.


The curly line was produced by an electron that was struck by one of twelve passing beam particles in a liquid hydrogen bubble chamber. It curves in an applied magnetic field and loses energy rapidly, spiralling inwards.

The quantum field theory part happens at the vertex of the electron with the beam. The track of the electron can be completely fitted using classical electromagnetic theory.
Theoretically one could describe the path of the electron as creation and annihilation operators operating on the hydrogen molecules on their way, but it would be an immensely convoluted computation.
Further more there are no waves in QFT representations. The wave nature is in the probability of interaction that can be computed for the vertex, and does not extend to all space after the interaction.
So there is no reason to expect any space  related effects.
