According to Buddhism, is it me who is getting punished or rewarded in next life for my deeds in this life?
Neither You nor Anyone else.
It is not you, because you are dying and reborning with very very short time period all the time we live in Sansara. It is not anyone else because the result taker is a anyway a part of the series of dying and reborning cycle.
To understand this you have to understand components of a creature.
maximum number of components that a creature can have are two. They are body and mind. minimum number of components that a creature can have is one. That is mind.(Aruupa Brahmas) (So now at that moment you must realize that there is no soul to a creature.)
In descriptive Abhidhamma, mind is categorized to 4 components as Vedanā, Saṃjñā, Saṅkhāra, Vijñāna.
This image shows the components of the creature without considering time.
Mind is continues flow of born, existence, dying of Naama (Mindlet). mindlet or Naama is the smallest sub component of the mind. 17 mindlets make a mindlet group called Ruupa.
This image shows how Naamas are born, exist and die with transmitting energy to the next Naama.
This image shows the time intervals of one Naama. Naama's born time=exist time= dying time= t1.
Time interval between Dead Naama and Born start of Naama = t2. So at that very little time there is no visible mind. At that moment only body is exist. This is the thing called as anathma/anatta.
- There can be one mindlet in the mind at once.
- For a time of blink, trillions of mindlets born, exist and die (So one Naama exist less than nanoseconds).
- If creature consists of body and mind combination, it must be considered both to call that as a creature. (At creatures point of view I, my point of view me).
- If creature consists of only mind , it must be considered mind to call that as a creature. (At creatures point of view I, my point of view me).
- When consider a wheel, engine, chase individually cannot be called as CAR. Likewise, body or mind (When both are there) individually cannot be called as me or I.
- This rapid born, existance and deth of Naama can be seen in high meditation levels of vidhardhana meditation.
- Now you realize there is no soul or thing that can be called as me because even before a person say me or I there are trillions of born, existence, dying of Naama.
- When someone do a Karma, karma is completed in one Ruupa (consecutive 17 Naamas).
- After doing the karma that Ruupa is dead. but energy transmitted to next Ruupas.
- If creature made karma those Ruupas are dead at 17 Naama's time. So the creature did the karma is dead with Ruupa (But Body didn't dead so actual dead is not visible).
- When Karma get punished at proper time the creature's body also can be dead.
- When body dies we call it as real death.
- When Karma get punished the Ruupas did the karma is dead and body also can be dead.
- Karma is also get punished to Ruupas. Ruupas feels the senses according to the Karma.
- When Karma is get punished, punished Ruupas are not the Ruupas that done the Karma but Those Ruupas are generated from the same stream of Naama cycle. So Load Buddha have said that the Punished person is Neither You nor Anyone else.
The answer comes in the Acela Sutta (although this quote comes from here). Basically we cannot say that you are paying for your sins, nor that nobody is paying for the sins, as both views take the extreme ends of annihilationism and eternalism. Instead, we should approach it from the perspective of dependent origination.
Again, when the Buddha was asked by the naked ascetic Kassapa whether suffering was of one's own making or of another's or both or neither, the Buddha replied "Do not put it like that." When asked whether there was no suffering or whether the Buddha neither knew nor saw it, the Buddha replied that there was, and that he both knew and saw it. He then said "Kassapa, if one asserts that 'He who makes (it) feels (it): being one existent from the beginning, his suffering is of his own making,' then one arrives at eternalism. But if one asserts that one makes (it), another feels (it); being one existent crushed out by feeling, his suffering is of another's making,' then one arrives at annihilationism. Instead of resorting to either extreme a Tathaagata teaches the Dhamma by the middle way (by dependent origination)" (S. XII, 17/vol. ii, 20).
so many make it seem like some moral judgment ... and it's not.
karma is NOT some cosmic sense of moral retribution. it is merely the effects of cosmic momentum amidst the gazillions of intertwined cogs and wheels and gears. you do something with negative consequences then gear 2 goes CW driving shaft 4 parallel to cog 3 which turns CCW which affects 1,204,302,750 other cogs to turn CW and 2,340,369 gears to turn CW at 45 degrees et al. THAT is karma.
The Buddha did not teach what the questioner is inferring.
The Buddha kept mundane dhamma & supramundane dhamma distinctly separate, as explained in MN 117 about the two sorts of right view.
The ideas in the question are ideas created by others at later time.
In other words, what is 'reborn' is a 'self' rather than something 'not-self' ('anatta').
'Rebirth' means the re-arising of self-view.
Therefore, what is re-born is always the idea of 'self'.
Please read the suttas, accurately. The suttas always state 'a being' ('satta') or person ('puriso') is subject to rebirth due to their own kamma.
This noble disciple reflects thus: ‘I am (ahaṃ) not the only one who is the owner of one’s kamma, the heir of one’s kamma; who has kamma as one’s origin, kamma as one’s relative, kamma as one’s resort; who will be the heir of whatever kamma, good or bad, that one does. All beings (sattā) that come and go, that pass away and undergo rebirth, are owners of their kamma, heirs of their kamma; all have kamma as their origin, kamma as their relative, kamma as their resort; all will be heirs of whatever kamma, good or bad, that they do.’